Around 3-manifold groups
Winter Braids VIII (Marseille, 2018), Winter Braids Lecture Notes (2018), Exposé no. 2, 26 p.

This text is an expanded version of the minicourse given at the session Winter Braids VIII. The goal is to present some basic properties of 3-manifold groups and to give an overview of some of the major progress made in their study this last decade. It is mostly of expository nature and does not intend to cover the subject. I thank the Winter Braids organizers for their invitation and their kind patience whilst these notes were completed, and the referee for his careful reading and his suggestions which greatly improved the exposition.

DOI : 10.5802/wbln.22
Boileau, Michel 1

1 Aix-Marseille Univ., CNRS, Centrale Marseille, I2M 13453 Marseille, France
@article{WBLN_2018__5__A2_0,
     author = {Boileau, Michel},
     title = {Around 3-manifold groups},
     booktitle = {Winter Braids VIII (Marseille, 2018)},
     series = {Winter Braids Lecture Notes},
     note = {talk:2},
     pages = {1--26},
     publisher = {Winter Braids School},
     year = {2018},
     doi = {10.5802/wbln.22},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/wbln.22/}
}
TY  - JOUR
AU  - Boileau, Michel
TI  - Around 3-manifold groups
BT  - Winter Braids VIII (Marseille, 2018)
AU  - Collectif
T3  - Winter Braids Lecture Notes
N1  - talk:2
PY  - 2018
SP  - 1
EP  - 26
PB  - Winter Braids School
UR  - http://archive.numdam.org/articles/10.5802/wbln.22/
DO  - 10.5802/wbln.22
LA  - en
ID  - WBLN_2018__5__A2_0
ER  - 
%0 Journal Article
%A Boileau, Michel
%T Around 3-manifold groups
%B Winter Braids VIII (Marseille, 2018)
%A Collectif
%S Winter Braids Lecture Notes
%Z talk:2
%D 2018
%P 1-26
%I Winter Braids School
%U http://archive.numdam.org/articles/10.5802/wbln.22/
%R 10.5802/wbln.22
%G en
%F WBLN_2018__5__A2_0
Boileau, Michel. Around 3-manifold groups, dans Winter Braids VIII (Marseille, 2018), Winter Braids Lecture Notes (2018), Exposé no. 2, 26 p. doi : 10.5802/wbln.22. http://archive.numdam.org/articles/10.5802/wbln.22/

[AF13] M. Aschenbrenner and S. Friedl, 3-manifold groups are virtually residually p, Mem. Amer. Math. Soc. 225 (2013), no. 1058. | DOI | MR | Zbl

[AFW15a] M. Aschenbrenner, S. Friedl and H. Wilton, 3-manifold groups, EMS Series Lect. Math. 20, Euro. Math. Soc., Zürich (2015). | DOI | Zbl

[AFW15b] M. Aschenbrenner, S. Friedl and H. Wilton, Decision problems for 3-manifolds and their fundamental groups, Geom. Topol. Monogr. 19 (2015), 201–236. | DOI | Zbl

[Ag04] I. Agol, Tameness of hyperbolic 3-manifolds, arXiv:math.GT/0405568.

[Ag08] I. Agol, Criteria for virtual fibering, J. Topol. 1 (2008), no. 2, 269–284. | DOI | MR | Zbl

[Ag13] I. Agol, The virtual Haken conjecture, with an appendix by I. Agol, D. Groves and J. Manning, Documenta Math. 18 (2013), 1045–1087. | Zbl

[AG73] R. B. F. T. Allenby and R. F. Gregorac, On locally extended residually finite groups, Conference on Group Theory, LNM 319, Springer-Verlag, Berlin-Heidelberg-New York, 1973, pp. 9–17. | DOI

[Al24] J.W. Alexander, On the subdivision of a 3-space by a polyhedron, Proc. Natl. Acad. Sci. USA 10 (1924) 6–8. | DOI

[B3MP10] L. Bessières, G. Besson, M. Boileau, S. Maillot, and J. Porti, Geometrisation of 3-manifolds, EMS Tracts in Mathematics 13 (2010). | DOI | Zbl

[BeM91] M. Bestvina and G. Mess, The Boundary of Negatively Curved Groups, J. AMS 4 (1991), 469–481 | DOI | MR | Zbl

[BeW10] N. Bergeron and D. Wise, A Boundary Criterion for Cubulation, A.J.M. 134 (2012), 843–859. | DOI | MR | Zbl

[BG04] M. Bridson and F. Grunewald, Grothendieck’s problems concerning profinite completions and representations of groups, Ann. of Math. (2) 160 (2004), no. 1, 359–373. | DOI | MR | Zbl

[BKS87] R. G. Burns, A. Karrass, and D. Solitar, A note on groups with separable finitely generated subgroups, Bull. Austral. Math. Soc. 36 (1987), 153–160. | DOI | MR | Zbl

[BMP03] M. Boileau, S. Maillot and J. Porti, Three-dimensional orbifolds and their geometric structures, Panorama et Synthèse 15 (2003), 167 pp. (2003). | DOI | Zbl

[BoB19] M. Boileau and S. Boyer, On Tits alternative for PD(3)-groups, in Low dimensional topology, hyperbolic manifolds and spectral geometry, An. Fac. Sciences Toulouse Sér. 6, Volume XXVIII (3) (2019), 397-415. | DOI | MR | Zbl

[BoFr15] M. Boileau and S. Friedl, The profinite completion of 3-manifold groups, fiberedness and the Thurston norm, arXiv:1505.07799, to appear in What’s Next?: The Mathematical Legacy of William P. Thurston, Princeton University Press.

[BoFr17] M. Boileau and S. Friedl, Grothendieck rigidity for 3-manifold groups, arXiv:1710.02746, to appear in Groups, Geometry & Dynamics. | DOI | MR | Zbl

[BoMe94] B. Bowditch and G. Mess, A 4-dimensional Kleinian group, Trans. Amer. Math. Soc. 344 (1994), 391–405. | DOI | MR | Zbl

[Bon86] F. Bonahon, Bouts des variétés hyperboliques de dimension 3, Annals of Math. 124 (1986), 71–158. | DOI | MR | Zbl

[Bon02] F. Bonahon, Geometric structures on 3-manifolds, Handbook of geometric topology, 93–164, North-Holland, Amsterdam, 2002. | DOI | Zbl

[Bow04] B. Bowditch, Planar groups and the Seifert conjecture, J. Reine Angew. Math. 576 (2004), 11–62. | DOI | MR | Zbl

[Bro82] K. Brown, Cohomology of groups, Graduate Texts in Mathematics 87, Springer Verlag (1982). | DOI | Zbl

[BrRe15] M. R. Bridson and A. W. Reid, Profinite rigidity, fibering, and the figure-eight knot, arXiv:1505.07886, to appear in What’s Next?: The Mathematical Legacy of William P. Thurston, Princeton University Press.

[BRW17] M. R. Bridson , A. W. Reid and H; Wilton, Profinite rigidity and surface bundles over the circle, Bull. London Math. Soc. 49 (2017), 831–841. | DOI | MR | Zbl

[BrWi14] M. R. Bridson and H. Wilton, The isomorphism problem for profinite completions of finitely presented, residually finite groups, Groups Geom. Dyn., 8 (2014), 733–745. | DOI | MR | Zbl

[BrWi15] M. R. Bridson and H. Wilton, The triviality problem for profinite completions Invent. Math., 202 (2015), 839–874. | DOI | MR | Zbl

[CaGa06] D. Calegari and D. Gabai, Shrinkwrapping and the taming of hyperbolic3-manifolds, J.A.M.S. 19 (2006), 385–446. | DOI | Zbl

[CaJu94] A. Casson and D. Jungreis, Convergence group and Seifert fibered 3-manifolds, Invent. Math. 118(1994), 441–456. | DOI | MR | Zbl

[Can96] R. D. Canary, A covering theorem for hyperbolic 3-manifolds and its applications, Topology 35 (1996), 751–778. | DOI | MR | Zbl

[Can08] R. D. Canary, Marden’s Tameness Conjecture: history and applications, in Geometry, Analysis and Topology of Discrete groups, ed. by L. Ji, K. Liu, L. Yang and S.T. Yau, Higher Education Press (2008), 137–162. | Zbl

[Cas07] F. Castel, Centralisateurs d’éléments dans les PD(3) paires, Comm. Math. Helv. 82 (2007), 499–517. | DOI | Zbl

[Cav12] W. Cavendish, Finite-sheeted covering spaces and solenoids over 3-manifolds, PhD thesis, Princeton University, 2012.

[CaZu06] H. D. Cao and X. P. Zhu, A complete proof of the Poincaré and geometrization conjectures-application of the Hamilton-Perelman theory of the Ricci flow, Asian J. Math. 10 (2006), 165–492. | DOI | Zbl

[Cha07] R. Charney, An introduction to right-angled Artin groups, Geom. Dedicata 125 (2007), 141–158. | DOI | MR | Zbl

[Dav98] M.W. Davis, The cohomology of a Coxeter group with group rings coefficients, Duke Math. J. 91 (1998), 297–314. | DOI | MR | Zbl

[Deh10] M.  Dehn, Über die Topologie des dreidimensionalen Raumes, Math. Ann. 69 (1910), 137–168. | DOI | Zbl

[Deh12] M.  Dehn, Über unendliche diskontinuierliche Gruppen, Math. Ann. 71 (1912), 116–144. | DOI | Zbl

[Del95] T. Delzant, L’image d’un groupe dans un groupe hyperbolique, Comment. Math. Helv. 70 (1995), 267–284. | DOI | MR

[DeSt87] M.  Dehn, Papers on group theory and topology, translated and introduced by John Stillwell, Springer, 1987. | DOI | Zbl

[DFPR82] J. Dixon, E. Formanek, J. Poland and L. Ribes, Profinite completions and isomorphic finite quotients, J. Pure Appl. Algebra 23 (1982), no. 3, 227–231. | DOI | MR | Zbl

[dlH10] P.  de la Harpe, Topologie, théorie des groupes et problèmes de décision, Gaz. Math. 125 (2010), 41–75. | Zbl

[Dro87] C. Droms, Graph groups, coherence, and three-manifolds, J. Algebra 106 (1987), 484–489. | DOI | MR | Zbl

[DuSw00] M.J. Dunwoody and E. L. Swenson, The algebraic torus theorem, Inv. Math. 140 (2000), 605–637. | DOI | MR | Zbl

[Ec87] B. Eckmann, Poncaré duality groups of dimension two are surface groups, in Combinatorial Group Theory and Topology, Ann. of Math. Studies 111 (1987), 35–51. | DOI

[Ep61] D. Epstein, Finite presentations of groups and 3-manifolds, Quart. J. Math. Oxford 12 (1961), 205–212. | DOI | MR | Zbl

[FrKi14] S. Friedl and T. Kitayama, The virtual fibering theorem for 3-manifolds, L’Enseignement Mathématique 1 (2014), 79–107. | DOI | MR | Zbl

[Fun13] L. Funar, Torus bundles not distinguished by TQFT invariants, Geometry & Topology 17 (2013), 2289–2344. | DOI | MR | Zbl

[Ga85] D. Gabai, Simple loop theorem, J. Diff. Geom. 21 (1985), 143–149. | DOI | MR | Zbl

[Ga92] D. Gabai, Convergence groups are Fuchsian groups, Ann. of Math. 136 (1992), 447–510. | DOI | MR | Zbl

[Gar18] G. Gardam, Profinite rigidity in the SnapPea census, arXiv:1805.02697.

[GMW12] D. Groves, J.F. Manning and H. Wilton, Recognizing geometric 3-manifold groups using the word problem, arXiv:1210.2101.

[Gon75] F. González-Acuna, 3-dimensional open books, Lecture Notes, University of Iowa (1975), 12pp, available at http://www.oberlin.edu/faculty/jcalcut/ga.pdf.

[Gor95] C.McA. Gordon, Dehn filling: a survey, in Knot theory (Warsaw, 1995), Banach Center Publ. 42 (1998), Polish Acad. Sci., Warsaw. | DOI | MR | Zbl

[Gor04] C.McA. Gordon, Artin groups, 3-manifolds and coherence, Bol. Soc. Mat. Mexicana 10 (2004), Special Issue, 193–98. | DOI | MR | Zbl

[Gr70] A. Grothendieck, Représentations linéaires et compactification profinie des ´ groupes discrets, Manuscripta Math. 2 (1970), 375–396. | DOI | MR | Zbl

[Hai14] P. Haissinsky, Hyperbolic groups with planar boundaries, Invent. Math. 201 (2015), Volume 201, 239–307. | DOI | MR | Zbl

[Has99] J. Hass, Minimal surfaces in manifold with S 1 actions and the simple loop conjecture forSeifert fiber spaces, Proc. Amer. Math. Soc. 99 (1987), 383–388. | DOI | Zbl

[HaW08] F. Haglund and D. T. Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008), 1551–1620. | DOI | MR

[HaW10] F. Haglund and D. T. Wise,Coxeter groups are virtually special, Adv. Math. 224 (2010), 1890–1903. | DOI | MR | Zbl

[HeJa72] J. Hempel and W. Jaco, Fundamental groups of 3-manifolds which are extensions, Ann. of Math. 95 (1972), 86–98. | DOI | MR | Zbl

[Hem76] J. Hempel, 3-Manifolds, Ann. of Math. Studies, vol. 86, Princeton University Press, Princeton, NJ, 1976.

[Hem87] J. Hempel, Residual finiteness for 3-manifolds, Combinatorial group theory and topology, Ann. of Math. Stud. 111, Princeton Univ. Press 1987, 379–396. | DOI | Zbl

[Hem14] J. Hempel, Some 3-manifold groups with the same finite quotients, preprint (2014) arXiv:1409.3509.

[HeMe99] S.M. Hermiller and J. Meier, Artin groups, rewriting systems and three-manifolds, J. Pure Appl. Algebra 136 (1999), 141–156. | DOI | MR | Zbl

[Hil85] J. Hillman, Seifert fibre spaces and Poincaré duality groups, Math. Z. 190 (1985), 365–369. | DOI | Zbl

[Hil87] J. Hillman, Three dimensional Poincaré duality groups which are extensions, Math. Z. 195, (1987), 89–92. | DOI | Zbl

[Hil02] J. Hillman, Four-manifolds, geometries and knots Geom. Topol. Monogr. 5 (2002), Geom. Topol. Publ., Coventry. | Zbl

[Hil03] J. Hillman, Tits alternatives and low dimensional topology, J. Math. Soc. Japan 55 (2003),365–383. | DOI | MR | Zbl

[Hil06] J. Hillman, Centralizers and normalizers of subgroups of PD 3 -groups and open PD 3 -groups, J. Pure Appl. Alg. 204 (2006), 244–257. | Zbl

[Hil19] J. Hillman, Poincaré Duality in Dimension 3, to appear in MSP open book series.

[Jac80] W. Jaco, Lectures on three-manifold topology, CBMS Regional Conference Series in Mathematics, 43. American Mathematical Society, Providence, R.I. (1980). | DOI

[JaS79] W. Jaco and P. Shalen. Seifert fibered spaces in 3-manifolds, Mem. Amer. Math. Soc. 21 (1979), no. 220. | DOI | Zbl

[Joh79] K. Johannson, Homotopy Equivalences of 3-Manifolds with Boundaries, Lecture Notes in Mathematics, Vol. 761. Springer, Berlin (1979). | DOI | Zbl

[JZ17] A. Jaikin-Zapirain, Recogniton of being fibred in compact 3-manifolds, preprint (2019), available online at http://matematicas.uam.es/andrei.jaikin/. | DOI | MR

[KaK05] M. Kapovich and B. Kleiner, Coarse Alexander duality and duality groups, J. Diff. Geom. 69, (2005), 279–352. | DOI | MR | Zbl

[KaK07] M. Kapovich and B. Kleiner, The weak hyperbolization conjecture for 3-dimensional CAT(0)-groups, Groups Geom. Dyn. 1 (2007), 61–79. | DOI | MR | Zbl

[KaM12] J. Kahn, and V. Markovic, Immersing almost geodesic surfaces in a closed hyperbolic three manifold. Ann. Math. 175, 1127–1190. | DOI | MR | Zbl

[Kie18] D. Kielak, Residually finite rationally solvable group and virtual fibring, arXiv:1809.09386v1. | DOI | MR | Zbl

[KL08] B. Kleiner and J. Lott, Notes on Perelman’s papers, Geom. & Top. 12 (2008), 2587–2858. | DOI | MR | Zbl

[Kne29] H. Kneser, Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten, Jahresbericht der Deutschen Mathematiker Vereinigung 38 (1929), 248–260. | DOI | Zbl

[KrMr04] P. B. Kronheimer and T. S. Mrowka, Dehn surgery, the fundamental group and SU(2), Math. Res. Lett. 11 (2004), 741–754. | DOI | MR | Zbl

[Kro90] P. H. Kropholler, An analogue of the torus decomposition theorem for certain Poincaré duality groups, Proc. London Math. Soc. 60 (1990), 503–529. | DOI | Zbl

[Kup17] G Kuperberg, Algorithmic homeomorphism of 3–manifolds as a corollary of geometrization, preprint (2015) arXiv:1508.06720v4. | DOI | MR | Zbl

[Liu13] Y. Liu, Virtual cubulation of nonpositively curved graph manifolds, J. Topology 6 (2013), 793–822. | DOI | MR | Zbl

[LR98] D. Long and A. Reid, Simple quotients of hyperbolic 3-manifold groups, Proceedings Amer. Math. Soc. 126 (1998), 877–880. | DOI | Zbl

[LR11] D. D. Long and A. Reid, Grothendieck’s problem for 3-manifold groups, Groups, Geometry and Dynamics, 5 (2011), 479–499. | DOI | MR | Zbl

[Lus95] M. Lustig, Non-efficient torsion-free groups exist, Comm. Alg.23 (1995), 215–218. | DOI | MR | Zbl

[Mai01] S. Maillot, Quasi-isometries of groups, graphs and surfaces, Comment. Math. Helv 76 (2001), 20–60. | DOI | MR | Zbl

[Mai03] S. Maillot, Open 3-manifolds whose fundamental groups have infinite center, and a torus theorem for 3-orbifolds, Trans. Amer. Math. Soc. 355 (2003), 4595–4638. | DOI | Zbl

[Mar13] V. Markovic, Criterion for Cannon’s conjecture, Geometric and Functional Analysis, 23 (2013), 1035–1061. | DOI | MR | Zbl

[Mat03] S Matveev, Algorithmic topology and classification of 3-manifolds, Algorithms and Computation in Mathematics 9, Springer, Berlin (2003). | DOI | Zbl

[Mes01] G. Mess, The Seifert conjecture and groups which are coarse quasi-isometric to planes, Preprint 1986.

[Mes90] G. Mess, Examples of Poincaré duality groups, Proc. Amer. Math. Soc., 110 (1990), 1145–1146. | DOI | Zbl

[Mil62] J. Milnor, A unique decomposition theorem for 3-manifolds, Amer. J. Math. 84 (1962), 1–7. | DOI | MR | Zbl

[Mos73] G. D. Mostow, Strong rigidity of locally symmetric spaces, Ann. of Math. Stud. 78, Princeton University Press, Princeton, NJ, 1973. | DOI | Zbl

[MoT07] J. Morgan and G. Tian, Ricci Flow and the Poincaré Conjecture, Clay Mathematics Monographs 3, American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2007. | DOI | Zbl

[MoT14] J. Morgan and G. Tian, The geometrization conjecture, Clay Mathematics Monographs 5, American Mathematical Society, Providence, RI; Clay Mathematics Institute, Cambridge, MA, 2014. | DOI | Zbl

[Ner18] G. Nery, Profinite genus of fundamental groups of Sol and Nil 3-manifolds, arXiv:1811.07202. | DOI | MR | Zbl

[NS07] N. Nikolov and D. Segal, On finitely generated profinite groups I: Strong completeness and uniform bounds, Ann. of Math. 165 (2007), 171–236. | DOI | MR | Zbl

[Papa57] C. Papakyriakopoulos, On Dehn’s lemma and the asphericity of knots, Ann. of Math. 66 (1957), 1–26. | DOI | MR | Zbl

[Per02] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv:math.DG/0211159.

[Per03a] G. Perelman, Ricci flow with surgery on three-manifolds, arXiv:math.DG/0303109.

[Per03b] G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, arXiv : math.DG/0307245.

[Poin95] H. Poincaré, Analysis Situs, J. École Polytechnique, vol 1 (1895), 1–121.

[Pot94] L. Potyagailo, Finitely generated Kleinian groups in 3-space and 3-manifolds of infinite homotopy type, Trans. Amer. Math. Soc. 344 (1994), 57–77. | DOI | MR | Zbl

[Pre06] J-P. Préaux, Conjugacy problem in groups of oriented geometrizable 3-manifolds, Topology 45 (2006), 171–208. | DOI | MR | Zbl

[Pre16] J-P. Préaux, The Conjugacy problem in groups of non-orientable 3-manifolds, Groups Geom. Dyn. 10 (2016), 473–522. | DOI | MR | Zbl

[PT86] V. Platonov and O. Tavgen, On the Grothendieck problem of profinite completions of groups, Dokl. Akad. Nauk SSSR 288 (1986), no. 5, 1054–1058.

[PW18] P. Przytycki and D. Wise, Mixed 3-manifolds are virtually special, J. Amer. Math. Soc. 31 (2018), 319–347. | DOI | MR | Zbl

[PW14] P. Przytycki and D. Wise, Separability of embedded surfaces in 3-manifolds, Compositio Mathematica 150 (2014), 1623-1630. | DOI | MR | Zbl

[Re15] A. W. Reid, Profinite properties of discrete groups, Proceedings of Groups St Andrews 2013, L.M.S. Lecture Note Series 242 (2015), 73–104, Cambridge Univ. Press. | DOI | Zbl

[Re18] A. W. Reid, Profinite rigidity, Proc. Int. Cong. of Math. 2018, Rio de Janeiro, Vol 1, 1191–1214. | DOI

[Ri90] E. Rips, An example of non-LERF group which is a free product of LERF groups with an amagalmated cyclic subgroup, Israel J. Math., 70 1990. | DOI | MR | Zbl

[Rib17] L. Ribes, Profinite Graphs and Groups, Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge. A Series of Modern Surveys in Mathematics 66. Springer-Verlag, Berlin, 2017.

[RuSw90] J. H. Rubinstein and G. A Swarup, On Scott’s Core Theorem, Bull. London Math. Soc. 22 (1990), 495–498. | DOI | MR | Zbl

[RuWa98] J. H. Rubinstein and S. Wang , π 1 -injective surfaces in graph manifolds, Comment. Math. Helv. 73 (1998), 499–515. | DOI | Zbl

[RZ10] L. Ribes and P. Zalesskii, Profinite groups. Second edition, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics 40, Springer-Verlag, Berlin, 2010. | Zbl

[Sag95] M. Sageev. Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc. 71 (1995), 585–617. | DOI | MR | Zbl

[Sco73a] P. Scott, Finitely generated 3-manifold groups are finitely presented, J. London Math. Soc. (2) 6 (1973), 437–440. | DOI | Zbl

[Sco83a] P. Scott, The geometries of 3-manifolds, Bull. London Math. Soc. 15 (1983), 401–487. | DOI | MR | Zbl

[Sco73b] P. Scott, Compact submanifolds of 3-manifolds, J. London Math. Soc. (2) 7 (1973), 246–250. | DOI | Zbl

[Sco83b] P. Scott, There are no fake Seifert fibre spaces with infinite π 1 , Ann. of Math. (2) 117 (1983), no. 1, 35–70. | DOI | MR | Zbl

[ScSh14] P. Scott and H. Short, The homeomorphism problem for closed 3-manifolds, Algebr. Geom. Topol. 14 (2014), 2431–2444. | DOI | MR | Zbl

[Sel95] Z. Sela, The isomorphism problem for hyperbolic groups, I, Ann. of Math. 141 (1995), 217–283. | DOI | MR | Zbl

[Ser97] J.-P. Serre, Galois cohomology, Springer-Verlag, Berlin, 1997. | DOI

[Sta60] J. Stallings, On the Loop Theorem, Ann. of Math. 72 (1960), 12–19. | DOI | MR | Zbl

[Sta62] J. Stallings, On fibering certain 3–manifolds, 1962 Topology of 3–manifolds and related topics (Proc. The Univ. of Georgia Institute, 1961) pp. 95–100 Prentice-Hall, Englewood Cliffs, N.J. (1962). | DOI

[Sta63] J. Stallings, On the recursiveness of sets of presentations of 3-manifold groups, Fund. Math. 51 1962/1963, 191–194. | DOI | MR | Zbl

[Sta66] J. Stallings, How not to prove the Poincaré Conjecture, Topology Seminar, Wisconsin, 1965, Ann. of Math. Studies 60, Princeton Univ. Press (1966), 83–88. | DOI | Zbl

[Sta71] J. Stallings, Group theory and three-dimensional manifolds, New Haven and London, Yale University Press, 1971. | Zbl

[Ste72] P. F. Stebe, Conjugacy Separability of groups of integer matrices, Proc. Amer. Math. Soc. 32 (1972) 1–7. | DOI | MR | Zbl

[Tho84] C.B. Thomas, Splitting theorems for certain PD3 groups, Math. Z. 186 (1984), 201–209. | DOI | Zbl

[Tho95] C.B. Thomas, 3-manifolds and PD(3)-groups, in Novikov conjectures, index theorems and rigidity, Vol. 2, London Math. Soc. Lecture Note Ser. 227, Cambridge Univ. Press, Cambridge, 1995, 301–308. | DOI | Zbl

[Thu79] W.P. Thurston, The geometry and topology of three-manifolds, Princeton University course notes, available at http://www.msri.org/publications/books/gt3m/ (1980).

[Thu97] W.P. Thurston, Three-dimensional geometry and topology. Vol. 1. Princeton Mathematical Press, Princeton, NJ, 1997. | DOI | Zbl

[Tuk88] P. Tukia, Homeomorphic conjugates of Fuchsian groups, J. Reine Angew. Math. 391 (1988), 1–54. | DOI | MR | Zbl

[Tur84] V. G. Turaev, Fundamental groups of three-dimensional manifolds and Poincaré duality, Proc. Steklov Institute Math. 4 (1984), 249–257.

[Uek18] , J. Ueki, The profinite completions of knot groups determine the Alexander polynomials, Algebr. Geom. Topol. 18 18 (2018), 3013–3030. | DOI | MR | Zbl

[Wa03] C.T.C. Wall, The geometry of abstract groups and their splittings, Rev. Mat. Complut. 16 (2003), 5–101. | DOI | MR | Zbl

[Wa04] C.T.C. Wall, Poincaré duality in dimension 3, Geom. Topol. Monogr. 7 (2004), Proceedings of the Casson Fest, Geom. Topol. Publ., Coventry, 1–26. | DOI | Zbl

[Wal68] F. Waldhausen, On irreducible 3-manifolds which are sufficiently large, Ann. of Math. (2) 87 (1968), 56–88. | Zbl

[Wh87] W. Whitten, Knot complements and groups, Topology 26 (1987), no. 1, 41–44. | DOI | MR | Zbl

[Wi09] D. Wise, The structure of groups with a quasi-convex hierarchy, Electronic Res. Ann. Math. Sci 16 (2009), 44–55. | DOI | MR | Zbl

[Wi12] D. T. Wise, From riches to raags: 3-manifolds, right-angled Artin groups, and cubical geometry, CBMS Regional Conference Series in Mathematics, vol.117, Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 2012. | DOI | Zbl

[Wi17] , D. T. Wise, The structure of groups with quasiconvex hierarchy, Ann. of Math. Stud. to appear.

[Wil17] G. Wilkes, Profinite rigidity of Seifert fibre spaces, Geo. Dedicata, 188 (2017), 141-163. | DOI | MR | Zbl

[Wil18a] G. Wilkes, Profinite rigidity of graph manifolds and JSJ decompositions of 3-manifolds, Journal of Algebra, 502 (2018), 538–587. | DOI | MR | Zbl

[Wil18b] G. Wilkes, Relative cohomology theory for profinite groups, Journal of Pure and Applied Algebra (2018). | DOI | MR | Zbl

[Wil18c] G. Wilkes, Profinite rigidity of graph manifolds, II: knots and mapping classes, arXiv preprint arXiv:1801.06386. | DOI | MR | Zbl

[WZ14] H. Wilton and P. Zalesskii, Profinite properties of graph manifolds, Geom. Dedicata 147 (2010), 29–45. | DOI | MR | Zbl

[WZ17a] H. Wilton and P. Zalesskii, Distinguishing geometries using finite quotients, Geometry and Topology, 21 (2017), 345–384. | DOI | MR | Zbl

[WZ17b] H. Wilton and P. Zalesskii, Profinite detection of 3-manifold decompositions, Compositio Mathematica, 155 (2019), no. 2, 246–259. | DOI | MR | Zbl

[Zem16] D. Zemke, The simple loop conjecture for 3-manifolds modeled on Sol, Algebraic and Geometric Topology 16 (2016), 3051–3071. | DOI | MR | Zbl

Cité par Sources :