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arXiv · 1411.7981

Combinatorial covers and vanishing of cohomology

Graham Denham·Alexander I. Suciu·Sergey Yuzvinsky
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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.

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BibTeXRIS

Graham Denham, Alexander I. Suciu, Sergey Yuzvinsky. 2014-11-28. Combinatorial covers and vanishing of cohomology. https://doi.org/10.1007/s00029-015-0196-8

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