Bestvina's normal form complex and the homology of Garside groups

Details Bestvina's normal form complex and the homology of Garside groups Bestvina's normal form complex and the homology of Garside groups

2002-02-22

arxiv.org/abs/math/0202228v2

Mathematics

Group Theory

14 pages, no figures, fixed file encoding errors

Scientific paper

A Garside group is a group admitting a finite lattice generating set D. Using techniques developed by Bestvina for Artin groups of finite type, we construct K(\pi,1)s for Garside groups. This construction shows that the (co)homology of any Garside group G is easily computed given the lattice D, and there is a simple sufficient condition that implies G is a duality group. The universal covers of these K(\pi,1)s enjoy Bestvina's weak non-positive curvature condition. Under a certain tameness condition, this implies that every solvable subgroup of G is virtually abelian.

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