2010/13 LEM Working Paper Series

The homotopy type of toric arrangements

Luca Moci, Simona Settepanella
Arrangement of hyperplanes, toric arrangements, CW complexes, Salvetti complex, Weyl groups, integer cohomology, Young Tableaux

  MSC 2010 Classifications
52C35, 32S22, 20F36,17B10

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 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 Ãn appearing in robotics.

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