Volume 23, issue 4 (2019)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 29
Issue 2, 549–862
Issue 1, 1–548

Volume 28, 9 issues

Volume 27, 9 issues

Volume 26, 8 issues

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Procedure
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1364-0380 (online)
ISSN 1465-3060 (print)
Author Index
To Appear
 
Other MSP Journals
Cubulable Kähler groups

Thomas Delzant and Pierre Py

Geometry & Topology 23 (2019) 2125–2164
Bibliography
1 I Agol, The virtual Haken conjecture, Doc. Math. 18 (2013) 1045 MR3104553
2 J Amorós, M Burger, K Corlette, D Kotschick, D Toledo, Fundamental groups of compact Kähler manifolds, 44, Amer. Math. Soc. (1996) MR1379330
3 W Ballmann, J Świątkowski, On groups acting on nonpositively curved cubical complexes, Enseign. Math. 45 (1999) 51 MR1703363
4 J Behrstock, R Charney, Divergence and quasimorphisms of right-angled Artin groups, Math. Ann. 352 (2012) 339 MR2874959
5 N Bergeron, F Haglund, D T Wise, Hyperplane sections in arithmetic hyperbolic manifolds, J. Lond. Math. Soc. 83 (2011) 431 MR2776645
6 N Bergeron, D T Wise, A boundary criterion for cubulation, Amer. J. Math. 134 (2012) 843 MR2931226
7 M R Bridson, On the semisimplicity of polyhedral isometries, Proc. Amer. Math. Soc. 127 (1999) 2143 MR1646316
8 M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
9 M R Bridson, J Howie, Subgroups of direct products of elementarily free groups, Geom. Funct. Anal. 17 (2007) 385 MR2322489
10 M R Bridson, J Howie, C F Miller III, H Short, The subgroups of direct products of surface groups, Geom. Dedicata 92 (2002) 95 MR1934013
11 M R Bridson, J Howie, C F Miller III, H Short, Subgroups of direct products of limit groups, Ann. of Math. 170 (2009) 1447 MR2600879
12 K S Brown, Cohomology of groups, 87, Springer (1994) MR1324339
13 M Burger, Fundamental groups of Kähler manifolds and geometric group theory, from: "Séminaire Bourbaki 2009/2010", Astérisque 339, Soc. Mat. de France (2011) 305 MR2906358
14 P E Caprace, M Sageev, Rank rigidity for CAT(0) cube complexes, Geom. Funct. Anal. 21 (2011) 851 MR2827012
15 J A Carlson, D Toledo, Harmonic mappings of Kähler manifolds to locally symmetric spaces, Inst. Hautes Études Sci. Publ. Math. 69 (1989) 173 MR1019964
16 F Catanese, Differentiable and deformation type of algebraic surfaces, real and symplectic structures, from: "Symplectic 4–manifolds and algebraic surfaces" (editors F Catanese, G Tian), Lecture Notes in Math. 1938, Springer (2008) 55 MR2441412
17 I Chatterji, T Fernós, A Iozzi, The median class and superrigidity of actions on CAT(0) cube complexes, J. Topol. 9 (2016) 349 MR3509968
18 M W Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983) 293 MR690848
19 M W Davis, T Januszkiewicz, Hyperbolization of polyhedra, J. Differential Geom. 34 (1991) 347 MR1131435
20 M Davis, T Januszkiewicz, R Scott, Nonpositive curvature of blow-ups, Selecta Math. 4 (1998) 491 MR1668119
21 O Debarre, Tores et variétés abéliennes complexes, 6, Soc. Mat. de France (1999) MR1767634
22 T Delzant, Trees, valuations and the Green–Lazarsfeld set, Geom. Funct. Anal. 18 (2008) 1236 MR2465689
23 T Delzant, L’invariant de Bieri–Neumann–Strebel des groupes fondamentaux des variétés kählériennes, Math. Ann. 348 (2010) 119 MR2657436
24 T Delzant, M Gromov, Cuts in Kähler groups, from: "Infinite groups: geometric, combinatorial and dynamical aspects" (editors L Bartholdi, T Ceccherini-Silberstein, T Smirnova-Nagnibeda, A Zuk), Progr. Math. 248, Birkhäuser (2005) 31 MR2195452
25 J.-P. Demailly, Complex analytic and differential geometry, book project (2012)
26 A Dimca, Ş Papadima, A I Suciu, Non-finiteness properties of fundamental groups of smooth projective varieties, J. Reine Angew. Math. 629 (2009) 89 MR2527414
27 C Druţu, M Kapovich, Geometric group theory, 63, Amer. Math. Soc. (2018) MR3753580
28 R Geoghegan, Topological methods in group theory, 243, Springer (2008) MR2365352
29 M Gromov, Hyperbolic groups, from: "Essays in group theory" (editor S M Gersten), Math. Sci. Res. Inst. Publ. 8, Springer (1987) 75 MR919829
30 M Gromov, Kähler hyperbolicity and L2–Hodge theory, J. Differential Geom. 33 (1991) 263 MR1085144
31 M Gromov, Metric structures for Riemannian and non-Riemannian spaces, 152, Birkhäuser (1999) MR1699320
32 M Gromov, R Schoen, Harmonic maps into singular spaces and p–adic superrigidity for lattices in groups of rank one, Inst. Hautes Études Sci. Publ. Math. 76 (1992) 165 MR1215595
33 M F Hagen, D T Wise, Cubulating hyperbolic free-by-cyclic groups: the general case, Geom. Funct. Anal. 25 (2015) 134 MR3320891
34 F Haglund, D T Wise, Special cube complexes, Geom. Funct. Anal. 17 (2008) 1551 MR2377497
35 C H Houghton, Ends of locally compact groups and their coset spaces, J. Austral. Math. Soc. 17 (1974) 274 MR0357679
36 V A Kaimanovich, W Woess, The Dirichlet problem at infinity for random walks on graphs with a strong isoperimetric inequality, Probab. Theory Related Fields 91 (1992) 445 MR1151805
37 I Kapovich, The nonamenability of Schreier graphs for infinite index quasiconvex subgroups of hyperbolic groups, Enseign. Math. 48 (2002) 359 MR1955607
38 M Kapovich, Energy of harmonic functions and Gromov’s proof of Stallings’ theorem, Georgian Math. J. 21 (2014) 281 MR3259072
39 A Kar, M Sageev, Ping pong on CAT(0) cube complexes, Comment. Math. Helv. 91 (2016) 543 MR3541720
40 N J Korevaar, R M Schoen, Sobolev spaces and harmonic maps for metric space targets, Comm. Anal. Geom. 1 (1993) 561 MR1266480
41 P H Kropholler, M A Roller, Relative ends and duality groups, J. Pure Appl. Algebra 61 (1989) 197 MR1025923
42 P Li, On the structure of complete Kähler manifolds with nonnegative curvature near infinity, Invent. Math. 99 (1990) 579 MR1032881
43 P Li, L F Tam, Harmonic functions and the structure of complete manifolds, J. Differential Geom. 35 (1992) 359 MR1158340
44 C Llosa Isenrich, Branched covers of elliptic curves and Kähler groups with exotic finiteness properties, Ann. Inst. Fourier (Grenoble) 69 (2019) 335
45 T Napier, M Ramachandran, Structure theorems for complete Kähler manifolds and applications to Lefschetz type theorems, Geom. Funct. Anal. 5 (1995) 809 MR1354291
46 T Napier, M Ramachandran, Hyperbolic Kähler manifolds and proper holomorphic mappings to Riemann surfaces, Geom. Funct. Anal. 11 (2001) 382 MR1837366
47 T Napier, M Ramachandran, Filtered ends, proper holomorphic mappings of Kähler manifolds to Riemann surfaces, and Kähler groups, Geom. Funct. Anal. 17 (2008) 1621 MR2377498
48 T Napier, M Ramachandran, L2 Castelnuovo–de Franchis, the cup product lemma, and filtered ends of Kähler manifolds, J. Topol. Anal. 1 (2009) 29 MR2649348
49 P Py, Coxeter groups and Kähler groups, Math. Proc. Cambridge Philos. Soc. 155 (2013) 557 MR3118420
50 M Sageev, Ends of group pairs and non-positively curved cube complexes, Proc. London Math. Soc. 71 (1995) 585 MR1347406
51 M Sageev, CAT(0) cube complexes and groups, from: "Geometric group theory" (editors M Bestvina, M Sageev, K Vogtmann), IAS/Park City Math. Ser. 21, Amer. Math. Soc. (2014) 7 MR3329724
52 P Scott, Ends of pairs of groups, J. Pure Appl. Algebra 11 (1977/78) 179 MR487104
53 C Simpson, Lefschetz theorems for the integral leaves of a holomorphic one-form, Compositio Math. 87 (1993) 99 MR1219454
54 Y T Siu, The complex-analyticity of harmonic maps and the strong rigidity of compact Kähler manifolds, Ann. of Math. 112 (1980) 73 MR584075
55 D T Wise, Cubulating small cancellation groups, Geom. Funct. Anal. 14 (2004) 150 MR2053602
56 D T Wise, From riches to raags : 3–manifolds, right-angled Artin groups, and cubical geometry, 117, Amer. Math. Soc. (2012) MR2986461