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Poset topology and homological invariants of algebras arising in algebraic combinatorics

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.
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https://hal.inria.fr/hal-01207594
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Stuart Margolis, Franco Saliola, Benjamin Steinberg. Poset topology and homological invariants of algebras arising in algebraic combinatorics. 26th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2014), 2014, Chicago, United States. pp.71-82. ⟨hal-01207594⟩

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