Cohomology ring of non-compact abelian arrangements
Algebraic Topology
2026-01-08 v2 Combinatorics
Abstract
We give a Orlik-Solomon type presentation for the cohomology ring of arrangements in a non-compact abelian Lie group. The new insight consists in comparing arrangements in different abelian groups. Our work is based on the Varchenko-Gelfand ring for real hyperplane arrangements and from that we deduce the cohomology rings of all other abelian arrangements. As by-product, we obtain a new proof of the Orlik-Solomon relations and De Concini-Procesi ones.
Keywords
Cite
@article{arxiv.2404.05588,
title = {Cohomology ring of non-compact abelian arrangements},
author = {Evienia Bazzocchi and Roberto Pagaria and Maddalena Pismataro},
journal= {arXiv preprint arXiv:2404.05588},
year = {2026}
}
Comments
24 pages, 4 figures