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