Deletion-restriction in toric arrangements

TL;DR

This paper extends the deletion-restriction technique to a class of toric arrangements, demonstrating that their complements have cohomology generated in degree one and are formal, advancing understanding in algebraic topology.

Contribution

It introduces a new class of toric arrangements where the cohomology algebra is generated in degree one and proves their complements are formal, using deletion-restriction.

Findings

Cohomology algebra of the complement is generated in degree 1 for the identified class.

The complement of these arrangements is proven to be formal in the sense of Sullivan.

Deletion-restriction is effectively applied to toric arrangements in this context.

Abstract

Deletion-restriction is a fundamental tool in the theory of hyperplane arrangements. Various important results in this field have been proved using deletion-restriction. In this paper we use deletion-restriction to identify a class of toric arrangements for which the cohomology algebra of the complement is generated in degree $1$. We also show that for these arrangements the complement is formal in the sense of Sullivan.