Fundamental groups of Kähler manifolds and geometric group theory

Burger, Marc

Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1022, 17 p.

MR Zbl

@incollection{AST_2011__339__305_0,
     author = {Burger, Marc},
     title = {Fundamental groups of {K\"ahler} manifolds and geometric group theory},
     booktitle = {S\'eminaire Bourbaki, volume 2009/2010, expos\'es 1012-1026},
     series = {Ast\'erisque},
     note = {talk:1022},
     pages = {305--321},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {339},
     year = {2011},
     mrnumber = {2906358},
     zbl = {1356.32001},
     language = {en},
     url = {https://www.numdam.org/item/AST_2011__339__305_0/}
}

TY  - CHAP
AU  - Burger, Marc
TI  - Fundamental groups of Kähler manifolds and geometric group theory
BT  - Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026
AU  - Collectif
T3  - Astérisque
N1  - talk:1022
PY  - 2011
SP  - 305
EP  - 321
IS  - 339
PB  - Société mathématique de France
UR  - https://www.numdam.org/item/AST_2011__339__305_0/
LA  - en
ID  - AST_2011__339__305_0
ER  -

%0 Book Section
%A Burger, Marc
%T Fundamental groups of Kähler manifolds and geometric group theory
%B Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026
%A Collectif
%S Astérisque
%Z talk:1022
%D 2011
%P 305-321
%N 339
%I Société mathématique de France
%U https://www.numdam.org/item/AST_2011__339__305_0/
%G en
%F AST_2011__339__305_0

Burger, Marc. Fundamental groups of Kähler manifolds and geometric group theory, dans Séminaire Bourbaki, volume 2009/2010, exposés 1012-1026, Astérisque, no. 339 (2011), Exposé no. 1022, 17 p. https://www.numdam.org/item/AST_2011__339__305_0/

Bibliographie
Cité par

[1] J. Amorós, M. Burger, K. Corlette, D. Kotschick & D. Toledo - Fundamental groups of compact Kähler manifolds, Mathematical Surveys and Monographs, vol. 44, Amer. Math. Soc., 1996. | MR | Zbl

[2] D. Arapura - "Geometry of cohomology support loci for local systems. I", J. Algebraic Geom. 6 (1997), p. 563-597. | MR | Zbl

[3] D. Arapura, P. Bressler & M. Ramachandran - "On the fundamental group of a compact Kähler manifold", Duke Math. J. 68 (1992), p. 477-488. | DOI | MR | Zbl

[4] D. Arapura & M. Nori - "Solvable fundamental groups of algebraic varieties and Kähler manifolds", Compositio Math. 116 (1999), p. 173-188. | DOI | MR | Zbl

[5] A. Beauville - "Annulation du $H^{1}$ pour les fibrés en droites plats", in Complex algebraic varieties (Bayreuth, 1990), Lecture Notes in Math., vol. 1507, Springer, 1992, p. 1-15. | DOI | MR | Zbl

[6] R. Bieri, W. D. Neumann & R. Strebel - "A geometric invariant of discrete groups", Invent. Math. 90 (1987), p. 451-477. | DOI | EuDML | MR | Zbl

[7] R. Bieri & R. Strebel - "Valuations and finitely presented metabelian groups", Proc. London Math. Soc. 41 (1980), p. 439-464. | DOI | MR | Zbl

[8] R. Bieri & R. Strebel, "Geometric invariants for discrete groups", unpublished monograph, 1992.

[9] E. Breuillard - "On uniform exponential growth for solvable groups", Pure Appl. Math. Q. 3 (2007), p. 949-967. | DOI | MR | Zbl

[10] A. Brudnyi - "Solvable matrix representations of Kähler groups", Differential Geom. Appl. 19 (2003), p. 167-191. | DOI | MR | Zbl

[11] F. Campana - "Remarques sur les groupes de Kähler nilpotents", Ann. Sci. École Norm. Sup. 28 (1995), p. 307-316. | DOI | EuDML | Numdam | MR | Zbl

[12] F. Campana, "Ensembles de Green-Lazarsfeld et quotients résolubles des groupes de Kähler", J. Algebraic Geom. 10 (2001), p. 599-622. | MR | Zbl

[13] E. M. Chirka - Complex analytic sets, Mathematics and its Applications (Soviet Series), vol. 46, Kluwer Academic Publishers Group, 1989. | MR | Zbl

[14] T. Delzant - "Trees, valuations and the Green-Lazarsfeld set", Geom. Funct. Anal. 18 (2008), p. 1236-1250. | DOI | MR | Zbl

[15] T. Delzant, "L'invariant de Bieri-Neumann-Strebel des groupes fondamentaux des variétés kählériennes", Math. Ann. 348 (2010), p. 119-125. | DOI | MR | Zbl

[16] T. Delzant & M. Gromov - "Cuts in Kähler groups", in Infinite groups: geometric, combinatorial and dynamical aspects, Progr. Math., vol. 248, Birkhäuser, 2005, p. 31-55. | MR | Zbl

[17] A. Dimca & A. I. Suciu - "Which $3$ -manifold groups are Kähler groups?", J. Eur. Math. Soc. (JEMS) 11 (2009), p. 521-528. | DOI | EuDML | MR | Zbl

[18] R. E. Gompf - "A new construction of symplectic manifolds", Ann. of Math. 142 (1995), p. 527-595. | DOI | MR | Zbl

[19] M. Green & R. Lazarsfeld - "Deformation theory, generic vanishing theorems, and some conjectures of Enriques, Catanese and Beauville", Invent. Math. 90 (1987), p. 389-407. | DOI | EuDML | MR | Zbl

[20] M. Green & R. Lazarsfeld, "Higher obstructions to deforming cohomology groups of line bundles", J. Amer. Math. Soc. 4 (1991), p. 87-103. | DOI | MR | Zbl

[21] M. Gromov - "Sur le groupe fondamental d'une variété kählérienne", C. R. Acad. Sci. Paris Sér. I Math. 308 (1989), p. 67-70. | MR | Zbl

[22] M. Gromov, "Kähler hyperbolicity and $L_{2}$ -Hodge theory", J. Differential Geom. 33 (1991), p. 263-292. | DOI | MR | Zbl

[23] J. R. J. Groves - "Soluble groups with every proper quotient polycyclic", Illinois J. Math. 22 (1978), p. 90-95. | MR | Zbl

[24] F. E. A. Johnson & E. G. Rees - "On the fundamental group of a complex algebraic manifold", Bull. London Math. Soc. 19 (1987), p. 463-466. | DOI | MR | Zbl

[25] L. Katzarkov - "Nilpotent groups and universal coverings of smooth projective varieties", J. Differential Geom. 45 (1997), p. 336-348. | DOI | MR | Zbl

[26] B. Klingler - "Kaehler groups and duality", preprint arXiv: 1005.2836.

[27] B. Klingler, "On the cohomology of Kaehler groups", preprint arXiv: 1005.2835.

[28] B. Klingler, V. Koziarz & J. Maubon - "On the second cohomology of Kaehler groups", preprint arXiv: 1004.3130. | MR

[29] J. Kollár - Shafarevich maps and automorphic forms, M. B. Porter Lectures, Princeton Univ. Press, 1995. | DOI | MR | Zbl

[30] D. Mcduff & D. Salamon - Introduction to symplectic topology, Oxford Math. Monographs, The Clarendon Press Oxford Univ. Press, 1998. | MR | Zbl

[31] T. Napier & M. Ramachandran - "Hyperbolic Kähler manifolds and proper holomorphic mappings to Riemann surfaces", Geom. Funct. Anal. 11 (2001), p. 382-406. | DOI | MR | Zbl

[32] T. Napier & M. Ramachandran, "Filtered ends, proper holomorphic mappings of Kähler manifolds to Riemann surfaces, and Kähler groups", Geom. Funct. Anal. 17 (2008), p. 1621-1654. | DOI | MR | Zbl

[33] R. Pink & D. Roessler - "A conjecture of Beauville and Catanese revisited", Math. Ann. 330 (2004), p. 293-308. | DOI | MR | Zbl

[34] D. J. S. Robinson - A course in the theory of groups, Graduate Texts in Math., vol. 80, Springer, 1996. | MR | Zbl

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

[36] P. Scott - "Ends of pairs of groups", J. Pure Appl. Algebra 11 (1977/78), p. 179-198. | DOI | MR | Zbl

[37] J-P. Serre - "Sur la topologie des varietés algébriques en caractéristique $p$ ", in Symposium internacional de topología algebraica, International symposium on algebraic topology, Universidad Nacional Autónoma de México and UNESCO, Mexico City, 1958, p. 24-53. | MR | Zbl

[38] J-P. Serre, "Arbres, amalgames, $S L_{2}$ ", Astérisque 46 (1977). | Numdam | MR | Zbl

[39] C. Simpson - "Lefschetz theorems for the integral leaves of a holomorphic one-form", Compositio Math. 87 (1993), p. 99-113. | EuDML | Numdam | MR | Zbl

[40] C. Simpson, "Subspaces of moduli spaces of rank one local systems", Ann. Sci. École Norm. Sup. 26 (1993), p. 361-401. | DOI | EuDML | Numdam | MR | Zbl

[41] D. Toledo - "Examples of fundamental groups of compact Kähler manifolds", Bull. London Math. Soc. 22 (1990), p. 339-343. | DOI | MR | Zbl

[42] D. Toledo, "Projective varieties with non-residually finite fundamental group", Publ. Math. I.H.É.S. 77 (1993), p. 103-119. | DOI | EuDML | Numdam | MR | Zbl

[43] C. Voisin - Hodge theory and complex algebraic geometry. I, Cambridge Studies in Advanced Math., vol. 76, Cambridge Univ. Press, 2002. | MR | Zbl

[44] C. Voisin, "On the homotopy types of compact Kähler and complex projective manifolds", Invent. Math. 157 (2004), p. 329-343. | DOI | MR | Zbl

[45] D. T. Wise - "Cubulating small cancellation groups", Geom. Funct. Anal. 14 (2004), p. 150-214. | DOI | MR | Zbl