Toric Arrangements

Abstract

This thesis addresses some fundamental questions on the topology of toric arrangement complements. We prove two main result which generalize well known results about hyperplane arrangements. Namely, we define a Salvetti complex for toric arrangements and prove that it encodes the topology of the complement of the corresponding arrangement. Then we use the same complex to prove that complements of toric arrangements are minimal spaces and therefore have no torsion in homology and cohomology. In doing this we use a number of combinatorial tools. In fact, we need to extend some of the usual notions of combinatorial topology, to adapt them to our purposes.