Weighted sheaves and homology of Artin groups

Abstract

In this paper we expand the theory of weighted sheaves over posets, and use it to study the local homology of Artin groups. First, we use such theory to relate the homology of classical braid groups with the homology of certain independence complexes of graphs. Then, in the context of discrete Morse theory on weighted sheaves, we introduce a particular class of acyclic matchings. Explicit formulas for the homology of the corresponding Morse complexes are given, in terms of the ranks of the associated incidence matrices. We use such method to perform explicit computations for the new affine case ${\tilde{C}}_n$, as well as for the cases $A_n$, $B_n$ and ${\tilde{A}}_n$ (which were already done before by different methods).

References in corpus (3)

• Cohomology of Artin groups of type tilde{A}_n, B_n and applications
• Some topological problems on the configuration spaces of Artin and Coxeter groups
• On the classifying space of Artin monoids

Cited by in corpus (8)

• Proof of the $K(\pi ,1)$ conjecture for affine Artin groups
• Discrete Morse Theory for Weighted Simplicial Complexes
• Chordal graphs, higher independence and vertex decomposable complexes
• Combinatorial and Topological Aspects of Path Posets, and Multipath Cohomology
• Topology of Clique Complexes of Line Graphs
• Higher Independence Complexes of graphs and their homotopy types
• On the local homology of Artin groups of finite and affine type
• Graded Betti numbers of a hyperedge ideal associated to join of graphs