English

Combinatorial covers and vanishing of cohomology

Algebraic Topology 2016-08-31 v2 Algebraic Geometry Combinatorics

Abstract

We use a Mayer-Vietoris-like spectral sequence to establish vanishing results for the cohomology of complements of linear and elliptic hyperplane arrangements, as part of a more general framework involving duality and abelian duality properties of spaces and groups. In the process, we consider cohomology of local systems with a general, Cohen-Macaulay-type condition. As a result, we recover known vanishing theorems for rank-1 local systems as well as group ring coefficients, and obtain new generalizations.

Keywords

Cite

@article{arxiv.1411.7981,
  title  = {Combinatorial covers and vanishing of cohomology},
  author = {Graham Denham and Alexander I. Suciu and Sergey Yuzvinsky},
  journal= {arXiv preprint arXiv:1411.7981},
  year   = {2016}
}

Comments

34 pages. To appear in Selecta Mathematica