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 homotopy equivalent to the arrangement complement, 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 appearing in robotics.

The homotopy type of toric arrangements

SETTEPANELLA S
2011-01-01

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 homotopy equivalent to the arrangement complement, 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 appearing in robotics.
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http://www.sciencedirect.com/science/article/pii/S0022404910002598
Arrangement of hyperplanes, toric arrangements, CW complexes, Salvetti complex, Weyl groups, integer cohomology, Young Tableaux
MOCI L; SETTEPANELLA S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1843062
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