The Koszul property as a topological invariant and measure of singularities

Hal Sadofsky and Brad Shelton

Vol. 252 (2011), No. 2, 473–486

DOI: 10.2140/pjm.2011.252.473

Abstract

Cassidy, Phan and Shelton have associated to any regular cell complex X a quadratic K-algebra R(X). They gave a combinatorial solution to the question of when this algebra is Koszul. The algebra R(X) is a combinatorial invariant but not a topological invariant. We show that, nevertheless, the property that R(X) be Koszul is a topological invariant.

In the process, we establish some conditions on the types of local singularities that can occur in cell complexes X such that R(X) is Koszul, and more generally in cell complexes that are pure and connected by codimension-one faces.

Keywords

Koszul algebras, singularities

Mathematical Subject Classification 2000

Primary: 16S37, 58K65

Milestones

Received: 12 November 2009

Revised: 13 November 2009

Accepted: 5 May 2010

Published: 29 October 2011