Regular neighbourhoods and canonical decompositions for groups

Scott, Peter ; Swarup, Gadde A.

Astérisque, no. 289 (2003) , 239 p.

MR Zbl | 1 citation dans Numdam

@book{AST_2003__289__R1_0,
     author = {Scott, Peter and Swarup, Gadde A.},
     title = {Regular neighbourhoods and canonical decompositions for groups},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {289},
     year = {2003},
     mrnumber = {2032389},
     zbl = {1036.20028},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2003__289__R1_0/}
}

TY  - BOOK
AU  - Scott, Peter
AU  - Swarup, Gadde A.
TI  - Regular neighbourhoods and canonical decompositions for groups
T3  - Astérisque
PY  - 2003
IS  - 289
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/AST_2003__289__R1_0/
LA  - en
ID  - AST_2003__289__R1_0
ER  -

%0 Book
%A Scott, Peter
%A Swarup, Gadde A.
%T Regular neighbourhoods and canonical decompositions for groups
%S Astérisque
%D 2003
%N 289
%I Société mathématique de France
%U http://archive.numdam.org/item/AST_2003__289__R1_0/
%G en
%F AST_2003__289__R1_0

Scott, Peter; Swarup, Gadde A. Regular neighbourhoods and canonical decompositions for groups. Astérisque, no. 289 (2003), 239 p. http://numdam.org/item/AST_2003__289__R1_0/

Bibliographie
Cité par

[1] S. A. Adeleke & P. M. Neumann Relations related to betweenness: their structure and automorphisms, Mem. Amer. Math. Soc., vol. 623, American Mathematical Society, Providence, RI, 1998. | MR | Zbl

[2] H. Bass Covering theory for graphs of groups, J. Pure Appl. Algebra 89 (1993), no. 1-2, p. 3-47. | MR | Zbl | DOI

[3] G. M. Bergman - On groups acting on locally finite graphs, Ann. of Math. 88 (1968), p. 335-340. | MR | Zbl | DOI

[4] M. Bestvina & M. Feighn Bounding the complexity of simplicial actions on trees, Invent. Math. 103 (1991), p. 145-186. | MR | Zbl | DOI

[5] B. H. Bowditch Cut points and canonical splittings of hyperbolic groups, Acta Math. 180 (1998), p. 145-186. | MR | Zbl | DOI

[6] B. H. Bowditch, Connectedness properties of limit sets, Trans. Amer. Math. Soc. 351 (1999), p. 3673-3686. | MR | Zbl | DOI

[7] B. H. Bowditch, Treelike structures arising from continua and convergence groups, Mem. Amer. Math. Soc., vol. 662, American Mathematical Society, Providence, RI, 1999. | MR | Zbl

[8] B. H. Bowditch, Splittings of finitely generated groups over two-ended subgroups, Trans. Amer. Math. Soc. 354 (2002), no. 3, p. 1049-1078. | MR | Zbl | DOI

[9] D. E. Cohen - Groups of cohomological dimension one, Lect. Notes in Math., vol. 245, Springer-Verlag, Berlin, 1972. | MR | Zbl

[10] W. Dicks & M. J. Dunwoody - Groups acting on graphs, Cambridge Studies in Advanced Mathematics, vol. 17, Cambridge University Press, 1989. | MR | Zbl

[11] M. J. Dunwoody - Accessibility and groups of cohomological dimension one, Proc. London Math. Soc. (3) 38 (1979), p. 193-215. | MR | Zbl | DOI

[12] M. J. Dunwoody, The accessibility of finitely presented groups, Invent. Math. 81 (1985), p. 449-457. | MR | Zbl | EuDML | DOI

[13] M. J. Dunwoody & M. Roller - Splittings of groups over polycyclic by finite subgroups, Bull. London Math. Soc. 25 (1993), p. 29-36. | MR | Zbl | DOI

[14] M. J. Dunwoody & M. E. Sageev JSJ-splittings for finitely presented groups over slender groups, Invent. Math. 135 (1999), p. 25-44. | MR | Zbl | DOI

[15] M. J. Dunwoody & E. Swenson - The Algebraic Torus Theorem, Invent. Math. 140 (2000), p. 605-637. | MR | Zbl | DOI

[16] M. Forester - On uniqueness of JSJ decompositions of finitely generated groups, Comment. Math. Helv., to appear. | MR | Zbl

[17] M. Forester, Deformation and rigidity of simplicial group actions on trees, Geom. Topol. 6 (2002), p. 219-267. | MR | Zbl | EuDML | DOI

[18] M. H. Freedman, J. Hass & P. Scott - Closed geodesics on surfaces, Bull. London Math. Soc. 14 (1982), p. 385-391. | MR | Zbl | DOI

[19] M. H. Freedman, Least area incompressible surfaces in 3-manifolds, Invent. Math. 71 (1983), p. 609-642. | MR | Zbl | EuDML | DOI

[20] K. Fujiwara & P. Papasoglu - JSJ-decompositions for finitely presented groups and complexes of groups, Preprint, 1997. | Zbl

[21] R. Geoghegan - Topological Methods in Group Theory, book to appear. | MR | Zbl | DOI

[22] V. Guirardel A very short proof of Forester's rigidity result, Geom. Topol. 7 (2003), p. 321-328. | MR | Zbl | EuDML | DOI

[23] G. Higman Subgroups of finitely presented groups, Proc. Roy. Soc. London Ser. A 262 (1961), p. 455-475. | MR | Zbl | DOI

[24] C. H. Houghton - Ends of locally compact groups and their quotient spaces, J. Aust. Math. Soc. 17 (1974), p. 274-284. | MR | Zbl | DOI

[25] W. Jaco & P. Shalen - Seifert fibered spaces in 3-manifolds, vol. 21, Mem. Amer. Math. Soc., no. 220, American Mathematical Society, Providence, RI, 1979. | MR | Zbl

[26] K. Johannson - Homotopy equivalences of 3-manifolds with boundary, Lect. Notes in Math., vol. 761, Springer-Verlag, 1979. | MR | Zbl

[27] P. H. Kropholler - An analogue of the torus decomposition theorem for certain Poincaré duality groups, Proc. London Math. Soc. (3) 60 (1990), p. 503-529. | MR | Zbl | DOI

[28] P. H. Kropholler, A group-theoretic proof of the torus theorem, in Geometric group theory, Vol. 1 (Sussex, 1991), London Math. Soc. Lecture Note Ser., vol. 181, Cambridge Univ. Press, Cambridge, 1993, p. 138-158. | MR | Zbl | DOI

[29] P. H. Kropholler & M. A. Roller - Splittings of Poincaré duality groups, Math. Z. 197 (1988), no. 3, p. 421-438. | MR | Zbl | EuDML | DOI

[30] P. H. Kropholler & M. A. Roller, Relative ends and duality groups, J. Pure Appl. Algebra 61 (1989), p. 197-210. | MR | Zbl | DOI

[31] P. H. Kropholler & M. A. Roller, Splittings of Poincaré duality groups III, J. London Math. Soc. (2) 39 (1989), no. 2, p. 271-284. | MR | Zbl | DOI

[32] B. Leeb & P. Scott - The characteristic submanifold in higher dimensions, Comment. Math. Helv. 75 (2000), p. 201-215. | Zbl | MR

[33] G. Mess - Examples of Poincaré duality groups, Proc. Amer. Math. Soc. 110 (1990), no. 4, p. 1145-1146. | MR | Zbl

[34] W. D. Neumann & G. A. Swarup Canonical decompositions of 3-manifolds, Geom. Topol. 1 (1997), p. 21-40. | MR | Zbl | EuDML | DOI

[35] G. Niblo - The singularity obstruction for group splittings, Topology Appl. 119 (2002), no. 1, p. 17-31. | MR | Zbl | DOI

[36] E. Rips & Z. Sela - Cyclic splittings of finitely presented groups and canonical JSJ-decomposition, Ann. of Math. (2) 146 (1997), p. 53-109. | MR | Zbl | DOI

[37] J. H. Rubinstein & S. Wang - $π_{1}$ -injective surfaces in graph manifolds, Comment. Math. Helv. 73 (1998), p. 499-515. | MR | Zbl | DOI

[38] M. Sageev - Codimension-1 subgroups and splittings of groups, J. Algebra 189 (1997), no. 2, p. 377-389. | MR | Zbl | DOI

[39] P. Scott - JSJ-decompositions of 3-manifolds, unpublished manuscript.

[40] P. Scott, Ends of pairs of groups, J. Pure Appl. Algebra 11 (1977), p. 179-198. | MR | Zbl | DOI

[41] P. Scott, A new proof of the Annulus and Torus Theorems, Amer. J. Math. 102 (1980), p. 241-277. | MR | Zbl | DOI

[42] P. Scott, The Symmetry of Intersection Numbers in Group Theory, Geom. Topol. 2 (1998), p. 11-29, Correction (ibid), 1998. | MR | Zbl | EuDML | DOI

[43] P. Scott & G. A. Swarup - An Algebraic Annulus Theorem, Pacific J. Math. 196 (2000), p. 461-506. | MR | Zbl | DOI

[44] P. Scott & G. A. Swarup, Splittings of groups and intersection numbers, Geom. Topol. 4 (2000), p. 179-218. | MR | Zbl | EuDML | DOI

[45] P. Scott & G. A. Swarup, Canonical splittings of groups and 3-manifolds, Trans. Amer. Math. Soc. 353 (2001), p. 4973-5001. | MR | Zbl | DOI

[46] P. Scott & G. A. Swarup, Regular Neighbourhoods and canonical decompositions for groups, Electron. Res. Announc. Amer. Math. Soc. 8 (2002), p. 20-28. | MR | Zbl | EuDML | DOI

[47] P. Scott & C. T. C. Wall - Topological methods in group theory, in Homological Group Theory, London Math. Soc. Lecture Notes Ser., vol. 36, Cambridge University Press, 1979, p. 137-214. | MR | Zbl | DOI

[48] Z. Sela Acylindrical accessibility for groups, Invent. Math. 129 (1997), p. 527-565. | MR | Zbl | DOI

[49] Z. Sela, Structure and rigidity in (Gromov) hyperbolic groups and rank 1 Lie groups, Geometric and Functional Anal. 7 (1997), p. 561-593. | MR | Zbl | DOI

[50] J.-P. Serre Arbres, amalgames, $S L_{2}$ , Astérisque, vol. 46, Société Mathématique de France, Paris, 1977. | MR | Zbl | Numdam

[51] J.-P. Serre, Trees, Springer-Verlag, Berlin-New York, 1980, Translated from the French by John Stillwell. | MR | Zbl

[52] J. R. Stallings - On torsion-free groups with infinitely many ends, Ann. of Math. 88 (1968), p. 312-334. | MR | Zbl | DOI

[53] J. R. Stallings, Group theory and three-dimensional manifolds, Yale Mathematical Monographs, vol. 4, Yale University Press, New Haven, Conn., 1971. | MR | Zbl

[54] E. Swenson Axial pairs and convergence groups on $S^{1}$ , Topology 39 (2000), p. 229-237. | MR | Zbl | DOI

[55] J. Tits - Sur le groupe des automorphismes d'un arbre, in Essays on topology and related topics (Mémoires dédiés a Georges de Rham) (A. Haefliger & R. Narasimhan, eds.), Springer-Verlag, New York-Berlin, 1970, p. 188-211. | MR | Zbl | DOI

[56] F. Waldhausen - On the determination of some bounded 3-manifolds by their fundamental groups alone, in Proc. of the International sympo. on Topology and its applications, Herceg-Novi, Yugoslavia, Beograd, 1969, p. 331-332. | Zbl