Poset topology and homological invariants of algebras arising in algebraic combinatorics

Stuart Margolis (1) , Franco Saliola (2) , Benjamin Steinberg (3)

1 Department of Mathematics [Bar-Ilan]
2 LaCIM - Laboratoire de combinatoire et d'informatique mathématique [Montréal]
3 CCNY - City College of New York [CUNY]

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.

Mots clés: left regular band; hyperplane arrangement; order complex; cohomology; poset topology; CW poset; Leray number; chordal graph; global dimension; hereditary algebra; (minimal) projective resolutions; Koszul algebra.

Domaines: Mathématique discrète [cs.DM]; Combinatoire [math.CO]

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, ⟨10.46298/dmtcs.2381⟩. ⟨hal-01207594⟩