A-infinity resolutions and the Golod property for monomial rings

TL;DR

This paper explores the A-infinity algebra structure on minimal free resolutions of monomial rings and establishes a combinatorial criterion for when such rings are Golod, linking algebraic and combinatorial properties.

Contribution

It introduces an A-infinity algebra structure on rooted resolutions and provides a combinatorial condition characterizing Golod monomial rings.

Findings

R is Golod iff the product on Tor^S(R,k) vanishes

Provides a necessary and sufficient combinatorial condition for Golodness

Establishes a link between algebraic structures and combinatorial properties

Abstract

Let R=S/I be a monomial ring whose minimal free resolution F is rooted. We describe an A-infinity algebra structure on F. Using this structure, we show that R is Golod if and only if the product on Tor^S(R,k) vanishes. Furthermore, we give a necessary and sufficient combinatorial condition for R to be Golod.