2010/13 | LEM Working Paper Series | |
The homotopy type of toric arrangements |
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Luca Moci, Simona Settepanella |
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Keywords | ||
Arrangement of hyperplanes, toric arrangements, CW complexes, Salvetti complex, Weyl groups, integer cohomology, Young Tableaux
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MSC 2010 Classifications | ||
52C35, 32S22, 20F36,17B10
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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 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 Ãn appearing in robotics.
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