The homotopy type of toric arrangements

Luca Moci and Simona Settepanella

LEM Papers Series from Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy

Abstract: 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 ℜ x , 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 à n appearing in robotics.

Keywords: Arrangement of hyperplanes; toric arrangements; CW complexes; Salvetti complex; Weyl groups; integer cohomology; Young Tableaux (search for similar items in EconPapers)
Date: 2010-07-27
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Persistent link: https://EconPapers.repec.org/RePEc:ssa:lemwps:2010/13

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