Combinatorial Topology of Toric arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2013 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.
Emanuele Delucchi +3 more
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The integer cohomology of toric Weyl arrangements [PDF]
, 2010 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 prove that if TW is the toric arrangement defined by the cocharacters lattice of a Weyl group W, then the
Simona Settepanella +1 more
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Morphisms and Order Ideals of Toric Posets
Mathematics, 2016 Toric posets are in some sense a natural “cyclic” version of finite posets in that they capture the fundamental features of a partial order but without the notion of minimal or maximal elements.
Matthew Macauley, Macauley Matthew
exaly +3 more sources
Erratum to "The integer cohomology algebra of toric arrangements"
, 2023 We point out two errors in the paper ``The integer cohomology algebra of toric arrangements'', Adv. Math., Vol. 313, pp. 746-802, 2017. The main error concerns Theorem 4.2.17.
Delucchi, Emanuele, Callegaro, Filippo
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An isomorphism between projective models of toric and hyperplane graphic arrangements
This paper presents a bridge between the theories of wonderful models associated with toric arrangements and wonderful models associated with hyperplane arrangements. In a previous work, the same authors noticed that the model of the toric arrangement of
Gaiffi, Giovanni +2 more
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Minimality of toric arrangements [PDF]
Journal of the European Mathematical Society, 2015 We prove that the complement of a toric arrangement has the homotopy type of a minimal CW-complex. As a corollary we deduce that the integer cohomology of these spaces is torsionfree. We apply discrete Morse theory to the toric Salvetti complex, providing a sequence of cellular collapses that leads to a minimal complex.
d'Antonio, Giacomo, Delucchi, Emanuele
openaire +3 more sources
Symmetry of f-Vectors of Toric Arrangements in General Position and Some Applications
The PUMP Journal of Undergraduate ResearchA toric hyperplane is the preimage of a point in a circle of a continuous surjective group homomorphism from the n-torus to the circle. A toric hyperplane arrangement is a finite collection of such hyperplanes.
Bergerová, Diana
core +4 more sources
The homotopy type of the polyhedral product for shifted complexes [PDF]
, 2013 We prove a conjecture of Bahri, Bendersky, Cohen and Gitler: if K is a shifted simplicial complex on n vertices,X1,...,Xn are pointed connected CW-complexes and CXi is the cone on Xi, then the polyhedral product determined by K and the pairs (C Xi , Xi )
Theriault, Stephen, Grbić, Jelena
core +1 more source
Cohomology of the toric arrangement associated with $$A_n$$ A n [PDF]
Journal of Fixed Point Theory and Applications, 2018 14 pages.
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A Salvetti Complex for Toric Arrangements and its Fundamental Group [PDF]
International Mathematics Research Notices, 2011 We describe a combinatorial model for the complement of a complexified toric arrangement by using nerves of acyclic categories. This generalizes recent work of Moci and Settepanella on thick toric arrangements. Moreover, we compute its fundamental group by finding a (finite) presentation.
d'Antonio, Giacomo, Delucchi, Emanuele
openaire +2 more sources