2012/10/26 by Michael Larsen, Larsen, Michael, Ayelet Lindenstrauss +1
Mathematics · #13D07 #52C35 #55U15 #Advanced Combinatorial Mathematics #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #math.CO #msc:13D07 #msc:52C35 #msc:55U15
paper · pdf · doi:10.48550/arxiv.1210.7254
15 pages
openalex publication_date 2012/10/26 · arxiv created 2012/11/12 · arxiv updated 2012/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the Coxeter cochain complex of a Coxeter group (G,S) with coefficients in a Z[G]-module A. This is closely related to the complex of simplicial cochains on the abstract simplicial complex I(S) of the commuting subsets of S. We give some representative computations of Coxeter cohomology and explain the connection between the Coxeter cohomology for groups of type A, the (singular) homology of certain configuration spaces, and the (Tor) homology of certain local Artin rings.