The homotopy type of toric arrangements

A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being the kernel of a character. In the present pa-per we build a CW-complex S homotopy equivalent to the arrangement complement RX, with a combinatorial description similar to that of the well-known Salvetti complex. If the toric arrangement is defined by a Weyl group, we also provide an algebraic description, very handy for co-homology computations. In the last part we give a description in terms of tableaux for a toric arrangement of type Ãn appearing in robotics. Keywords: Arrangement of hyperplanes, toric arrangements, CW complexes, Salvetti complex