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.

Keywords

• 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.
• [info.info-dm] computer science [cs]/discrete mathematics [cs.dm]
• [math.math-co] mathematics [math]/combinatorics [math.co]