## Algebraic & Geometric Topology

### $A_{\infty}$–resolutions and the Golod property for monomial rings

Robin Frankhuizen

#### Abstract

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

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 6 (2018), 3403-3424.

Dates
Revised: 16 April 2018
Accepted: 16 June 2018
First available in Project Euclid: 27 October 2018

https://projecteuclid.org/euclid.agt/1540605647

Digital Object Identifier
doi:10.2140/agt.2018.18.3403

Mathematical Reviews number (MathSciNet)
MR3868225

Zentralblatt MATH identifier
06990068

#### Citation

Frankhuizen, Robin. $A_{\infty}$–resolutions and the Golod property for monomial rings. Algebr. Geom. Topol. 18 (2018), no. 6, 3403--3424. doi:10.2140/agt.2018.18.3403. https://projecteuclid.org/euclid.agt/1540605647

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