Geometrization of 3-dimensional Coxeter group manifolds and Singer’s conjecture
نویسنده
چکیده
Associated to any Coxeter system (W,S), there is a labeled simplicial complex L and a contractible CW-complex ΣL (the Davis complex) on which W acts properly and cocompactly. ΣL admits a cellulation under which the nerve of each vertex is L. It follows that if L is a triangulation of S , then ΣL is a contractible n-manifold. We prove that a special case of the Singer conjecture for ΣL (on the vanishing of reduced l -homology except in the middle dimension) follows from Andreev’s theorem, which gives the necessary and sufficient conditions for a classical reflection group to act on H.
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Geometrization of 3-dimensional Coxeter orbifolds and Singer’s conjecture
Associated to any Coxeter system (W,S), there is a labeled simplicial complex L and a contractible CW-complex ΣL (the Davis complex) on which W acts properly and cocompactly. ΣL admits a cellulation under which the nerve of each vertex is L. It follows that if L is a triangulation of S, then ΣL is a contractible n-manifold. In this case, the orbit space, KL := ΣL/W , is a Coxeter orbifold. We p...
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