2002/02/22 by Ruth Charney, Charney, Ruth, John Meier +3 · 1 citation
Mathematics · #20F36 #20F65 (primary) #55P20 (Secondary) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:20F36 #msc:20F65 #msc:55P20
paper · pdf · doi:10.48550/arxiv.math/0202228
14 pages, no figures, fixed file encoding errors
openalex publication_date 2002/02/22 · arxiv created 2002/03/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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(π,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(π,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.