Algebraic & Geometric Topology

Cohomology of Coxeter groups with group ring coefficients: II

Michael W Davis, Jan Dymara, Tadeusz Januszkiewicz, and Boris Okun

Full-text: Open access

Abstract

For any Coxeter group W, we define a filtration of H(W;ZW) by W–submodules and then compute the associated graded terms. More generally, if U is a CW complex on which W acts as a reflection group we compute the associated graded terms for H(U) and, in the case where the action is proper and cocompact, for Hc(U).

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 3 (2006), 1289-1318.

Dates
Received: 10 April 2006
Revised: 28 June 2006
Accepted: 22 June 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796578

Digital Object Identifier
doi:10.2140/agt.2006.6.1289

Mathematical Reviews number (MathSciNet)
MR2253447

Zentralblatt MATH identifier
1153.20038

Subjects
Primary: 20F55: Reflection and Coxeter groups [See also 22E40, 51F15]
Secondary: 20C08: Hecke algebras and their representations 20E42: Groups with a $BN$-pair; buildings [See also 51E24] 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20J06: Cohomology of groups 57M07: Topological methods in group theory

Keywords
Coxeter group Hecke algebra building cohomology of groups

Citation

Davis, Michael W; Dymara, Jan; Januszkiewicz, Tadeusz; Okun, Boris. Cohomology of Coxeter groups with group ring coefficients: II. Algebr. Geom. Topol. 6 (2006), no. 3, 1289--1318. doi:10.2140/agt.2006.6.1289. https://projecteuclid.org/euclid.agt/1513796578


Export citation

References

  • N Bourbaki, Lie groups and Lie algebras. Chapters 4–6, Elements of Mathematics (Berlin), Springer, Berlin (2002)
  • K S Brown, Cohomology of groups, Graduate Texts in Mathematics 87, Springer, New York (1982)
  • M W Davis, Groups generated by reflections and aspherical manifolds not covered by Euclidean space, Ann. of Math. (2) 117 (1983) 293–324
  • M W Davis, The homology of a space on which a reflection group acts, Duke Math. J. 55 (1987) 97–104
  • M W Davis, The cohomology of a Coxeter group with group ring coefficients, Duke Math. J. 91 (1998) 297–314
  • M W Davis, J Dymara, T Januszkiewicz, B Okun, Weighted $L^2$-cohomology of Coxeter groups, preprint (2004)
  • M W Davis, J Meier, The topology at infinity of Coxeter groups and buildings, Comment. Math. Helv. 77 (2002) 746–766
  • J Dymara, T Januszkiewicz, Cohomology of buildings and their automorphism groups, Invent. Math. 150 (2002) 579–627
  • A Haefliger, Extension of complexes of groups, Ann. Inst. Fourier $($Grenoble$)$ 42 (1992) 275–311
  • D Kazhdan, G Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979) 165–184
  • L Solomon, A decomposition of the group algebra of a finite Coxeter group, J. Algebra 9 (1968) 220–239