Skip to Main content Skip to Navigation
Conference papers

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.
Document type :
Conference papers
Complete list of metadata
Contributor : Alain Monteil Connect in order to contact the contributor
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


Publisher files allowed on an open archive




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, ⟨10.46298/dmtcs.2374⟩. ⟨hal-01229686⟩



Record views


Files downloads