The homotopy type of toric arrangements - Luca Moci; Simona Settepanella (Scuola Superiore Sant'Anna, Laboratory of Economics and Management (LEM), 2010)
A toric arrangement is a finite set of hypersurfaces in a complex torus, every hypersurface being the kernel of a character. In the present paper 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 cohomology computations. In the last part we give a description in terms of tableaux for a toric arrangement of type An appearing in robotics.
Keywords: 330; Arrangement of hyperplanes; toric arrangements; CW complexes; Salvetti complex; Weyl groups; integer cohomology; Young Tableaux; Roboter; Künstliche Intelligenz; Objektorientierte Programmierung