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The homotopy type of toric arrangements

Author

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  • Luca Moci
  • Simona Settepanella

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.

Suggested Citation

  • Luca Moci & Simona Settepanella, 2010. "The homotopy type of toric arrangements," LEM Papers Series 2010/13, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  • Handle: RePEc:ssa:lemwps:2010/13
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    Keywords

    Arrangement of hyperplanes; toric arrangements; CW complexes; Salvetti complex; Weyl groups; integer cohomology; Young Tableaux;

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