Giacomo d'Antonio ; Emanuele Delucchi - Combinatorial Topology of Toric arrangements

dmtcs:2374 - Discrete Mathematics & Theoretical Computer Science, January 1, 2013, DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013) - https://doi.org/10.46298/dmtcs.2374
Combinatorial Topology of Toric arrangementsArticle

Authors: Giacomo d'Antonio 1; Emanuele Delucchi 1

  • 1 Fachbereich Mathematik und Informatik [Bremen]

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.


Volume: DMTCS Proceedings vol. AS, 25th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2013)
Section: Proceedings
Published on: January 1, 2013
Imported on: November 21, 2016
Keywords: Combinatorial topology,Toric arrangements,Discrete Morse theory,Torsion-freeness in homology.,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]

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