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arXiv · 1311.6680

Poset topology and homological invariants of algebras arising in algebraic combinatorics

Stuart Margolis·Franco Saliola·Benjamin Steinberg
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Abstract

We present a beautiful interplay between combinatorial topology and homological algebra for a class of monoids that arise naturally in algebraic combinatorics. We explore several applications of this interplay. For instance, we provide a new interpretation of the Leray number of a clique complex in terms of non-commutative algebra. Résumé. Nous présentons une magnifique interaction entre la topologie combinatoire et l'algèbre homologique d'une classe de monoïdes qui figurent naturellement dans la combinatoire algébrique. Nous explorons plusieurs applications de cette interaction. Par exemple, nous introduisons une nouvelle interprétation du nombre de Leray d'un complexe de clique en termes de la dimension globale d'une certaine algèbre non commutative.

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BibTeXRIS

Stuart Margolis, Franco Saliola, Benjamin Steinberg. 2013-11-26. Poset topology and homological invariants of algebras arising in algebraic combinatorics. https://arxiv.org/abs/1311.6680

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