Cohomology of hyperplane complements with group ring coefficients

2010/02/16 by Davis, Michael W, Januszkiewicz, Tadeusz, Leary, Ian J +1
#20J06 #32S22 #55N25 #57N65 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1002.3129

Abstract

We compute the cohomology with group ring coefficients of the complement of a finite collection of affine hyperplanes in a finite dimensional complex vector space. It is nonzero in exactly one degree, namely the degree equal to the rank of the hyperplane arrangement.

Related

• Hyperplane arrangements, M-tame polynomials and twisted cohomology
• The l²-cohomology of hyperplane complements
• The cohomology ring of the complement of a finite family of linear subspaces in a complex projective space
• Motivic cohomology of the complement of hyperplane arrangements
• Complements of hyperplane arrangements as posets of spaces