Record number :
1576908
Title of article :
ℓ2-homology of right-angled Coxeter groups based on barycentric subdivisions
Author/Authors :
Davis، نويسنده , , Michael W. and Okun، نويسنده , , Boris، نويسنده ,
Issue Information :
دوماهنامه با شماره پیاپی سال 2004
Pages :
6
From page :
197
To page :
202
Abstract :
Associated to any finite flag complex L there is a right-angled Coxeter group WL and a contractible cubical complex ΣL on which WL acts properly and cocompactly, and such that the link of each vertex is L. It follows that if L is a triangulation of Sn−1, then ΣL is a contractible n-manifold. We establish vanishing (in a certain range) of the reduced ℓ2-homology of ΣL in the case where L is the barycentric subdivision of a cellulation of a manifold. In particular, we prove the Singer Conjecture (on the vanishing of the reduced ℓ2-homology except in the middle dimension) in the case of ΣL where L is the barycentric subdivision of a cellulation of Sn−1, n=6,8.
Keywords :
Aspherical manifold , barycentric subdivision , ?2-homology , Coxeter group , ?2-Betti numbers
Journal title :
Topology and its Applications
Journal title :
Topology and its Applications
Serial Year :
2004
Link To Document :
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