The $\ell^2$-homology of even Coxeter groups

Details The $\ell^2$-homology of even Coxeter groups The $\ell^2$-homology of even Coxeter groups

2007-07-12

arxiv.org/abs/0707.1899v2

Mathematics

Geometric Topology

15 pages, 1 figure

Scientific paper

Given a Coxeter system (W,S), there is an associated CW-complex, Sigma, on
which W acts properly and cocompactly. We prove that when the nerve L of (W,S)
is a flag triangulation of the 3-sphere, then the reduced $\ell^2$-homology of
Sigma vanishes in all but the middle dimension.

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