The study of arrangements of subtori in the complex torus T = Cn is a recently thriving topic. It has some structural similarities with the theory of hyperplane arrangements, yet it bears its own peculiarities.
The Salvetti complex is a combinatorial model of the complement of a complexified real arrangement of hyperplanes. We take Salvetti's work as a stepping stone to develop a combinatorial model for the complement of a complex toric subspace arrangement, M := T\A, where A is the union of the subtori in the arrangement. More precisely, we prove that M is homotopy equivalent to the nerve of a combinatorially defined acyclic category. Then, we find a presentation of the fundamental group of M.
This is joint work with Giacomo D'Antonio of the University of Bremen.