Minimality of toric arrangements

TL;DR

This paper proves that the complement of a toric arrangement has a minimal CW complex homotopy type, leading to torsion-free integer cohomology, using Discrete Morse Theory for cellular collapses.

Contribution

It establishes the minimality of the CW complex for toric arrangement complements and demonstrates torsion-free cohomology, a novel application of Discrete Morse Theory in this context.

Findings

Complement of toric arrangements has minimal CW complex homotopy type

Integer cohomology of these spaces is torsion free

Discrete Morse Theory provides cellular collapses to minimal complexes

Abstract

We prove that the complement of a toric arrangement has the homotopy type of a minimal CW complex. As a corollary we obtain that the integer cohomology of these spaces is torsion free. We use Discrete Morse Theory, providing a sequence of cellular collapses that leads to a minimal complex.