Combinatorial generators for the cohomology of toric arrangements

TL;DR

This paper provides a new combinatorial method to describe the cohomology ring of the complement of complexified toric arrangements, correcting previous errors and advancing understanding in algebraic topology.

Contribution

It introduces a novel combinatorial framework for the cohomology of toric arrangements, rectifying earlier inaccuracies in the field.

Findings

New combinatorial description of cohomology ring

Correction of previous errors in cohomology algebra calculations

Enhanced understanding of toric arrangement topology

Abstract

We give a new combinatorial description of the cohomology ring structure of $H^*(M(\mathcal{A});\mathbb{Z})$ of the complement $M(\mathcal{A})$ of a real complexified toric arrangement $\mathcal{A}$ in $(\mathbb{C}^*)^d$. In particular, we correct an error in the paper ``The integer cohomology algebra of toric arrangements'', Adv. Math., 2017.