Volume 16, issue 4 (2016)

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

Volume 20
Issue 4, 1601–2143
Issue 3, 1073–1600
Issue 2, 531–1072
Issue 1, 1–529

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Ethics Statement
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
The fattened Davis complex and weighted $L^2$–(co)homology of Coxeter groups

Wiktor J Mogilski

Algebraic & Geometric Topology 16 (2016) 2067–2105
Bibliography
1 E M Andreev, On convex polyhedra of finite volume in Lobachevskii space, Mat. Sb. 12 (1971) 256 MR0273510
2 M Bestvina, The virtual cohomological dimension of Coxeter groups, from: "Geometric group theory, 1" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 181, Cambridge Univ. Press (1993) 19 MR1238512
3 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
4 J Cheeger, M Gromov, L2–cohomology and group cohomology, Topology 25 (1986) 189 MR837621
5 M W Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. 117 (1983) 293 MR690848
6 M W Davis, The geometry and topology of Coxeter groups, 32, Princeton Univ. Press (2008) MR2360474
7 M W Davis, J Dymara, T Januszkiewicz, J Meier, B Okun, Compactly supported cohomology of buildings, Comment. Math. Helv. 85 (2010) 551 MR2653692
8 M W Davis, J Dymara, T Januszkiewicz, B Okun, Weighted L2–cohomology of Coxeter groups, Geom. Topol. 11 (2007) 47 MR2287919
9 M W Davis, B Okun, Vanishing theorems and conjectures for the 2–homology of right-angled Coxeter groups, Geom. Topol. 5 (2001) 7 MR1812434
10 M W Davis, B Okun, Cohomology computations for Artin groups, Bestvina–Brady groups, and graph products, Groups Geom. Dyn. 6 (2012) 485 MR2961283
11 J Dodziuk, L2 harmonic forms on rotationally symmetric Riemannian manifolds, Proc. Amer. Math. Soc. 77 (1979) 395 MR545603
12 J Dymara, L2–cohomology of buildings with fundamental class, Proc. Amer. Math. Soc. 132 (2004) 1839 MR2051148
13 J Dymara, Thin buildings, Geom. Topol. 10 (2006) 667 MR2240901
14 J Dymara, T Januszkiewicz, Cohomology of buildings and their automorphism groups, Invent. Math. 150 (2002) 579 MR1946553
15 D B A Epstein, A Marden, Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces, from: "Analytical and geometric aspects of hyperbolic space" (editor D B A Epstein), London Math. Soc. Lecture Note Ser. 111, Cambridge Univ. Press (1987) 113 MR903852
16 J E Humphreys, Reflection groups and Coxeter groups, 29, Cambridge Univ. Press (1990) MR1066460
17 J Lott, W Lück, L2–topological invariants of 3–manifolds, Invent. Math. 120 (1995) 15 MR1323981
18 W Lück, L2–invariants : theory and applications to geometry and K–theory, 44, Springer (2002) MR1926649
19 B Okun, K Schreve, The L2–(co)homology of groups with hierarchies, preprint (2014) arXiv:1407.1340
20 G Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, preprint (2003) arXiv:math.DG/0307245
21 T A Schroeder, The l2–homology of even Coxeter groups, Algebr. Geom. Topol. 9 (2009) 1089 MR2511140
22 T A Schroeder, On the three-dimensional Singer conjecture for Coxeter groups, preprint (2009) arXiv:0909.0071
23 T A Schroeder, 2–homology and planar graphs, Colloq. Math. 131 (2013) 129 MR3078976