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Combinatorial Topology of Toric arrangements

Authors
  • d'Antonio, Giacomo
  • Delucchi, Emanuele
Publication Date
Jan 01, 2013
Source
HAL-UPMC
Keywords
Language
English
License
Unknown
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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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