The ` 2-homology of even Coxeter groups

@inproceedings{Schroeder2008The2,
  title={The ` 2-homology of even Coxeter groups},
  author={Timothy A. Schroeder},
  year={2008}
}
Given a Coxeter system (W, S), there is an associated CW-complex, denoted Σ(W, S) (or simply Σ), on which W acts properly and cocompactly. This is the Davis complex. L, the nerve of (W, S), is a finite simplicial complex. We prove that when (W, S) is an even Coxeter system and L is a flag triangulation of S, then the reduced `-homology of Σ vanishes in all but the middle dimension. In so doing, our main effort will be examining a certain subspace of Σ called the (S, t)-ruin, for some t ∈ S. To… CONTINUE READING

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