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Combinatorial Topology of Toric arrangements

Abstract : We prove that the complement of a complexified toric arrangement has the homotopy type of a minimal CW-complex, and thus its homology is torsion-free. To this end, we consider the toric Salvetti complex, a combinatorial model for the arrangement's complement. Using diagrams of acyclic categories we obtain a stratification of this combinatorial model that explicitly associates generators in homology to the "local no-broken-circuit sets'' defined in terms of the incidence relations of the arrangement. Then we apply a suitably generalized form of Discrete Morse Theory to describe a sequence of elementary collapses leading from the full model to a minimal complex.
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https://hal.inria.fr/hal-01229686
Contributor : Alain Monteil <>
Submitted on : Tuesday, November 17, 2015 - 10:19:56 AM
Last modification on : Tuesday, March 7, 2017 - 3:24:36 PM
Long-term archiving on: : Thursday, February 18, 2016 - 11:38:24 AM

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Giacomo d'Antonio, Emanuele Delucchi. Combinatorial Topology of Toric arrangements. 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013), 2013, Paris, France. pp.1161-1172. ⟨hal-01229686⟩

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