On the Euler-Poincaré characteristic of parallel toric arrangements

Abstract

Toric arrangements of maximal rank have been studied by the author in a paper that shows how the complement manifold of these arrangements is diffeomorphic to that of centered ones. In this work we turn our attention to toric arrangements of rank one, namely parallel toric arrangements. Our aim is to prove, by means of basic arguments of cohomology theory, that the Euler-Poincaré characteristic of the complement manifold of parallel toric arrangements can be computed in terms of those of the complement manifolds of the singular subtori that compose the arrangement.