Algebraic & Geometric Topology

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

Robin Frankhuizen

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Abstract

Let R=SI 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
Received: 11 October 2017
Revised: 16 April 2018
Accepted: 16 June 2018
First available in Project Euclid: 27 October 2018

Permanent link to this document
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

Subjects
Primary: 13D07: Homological functors on modules (Tor, Ext, etc.) 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series 16E45: Differential graded algebras and applications 55S30: Massey products

Keywords
Golod ring Poincaré series A-infinity algebra Massey products

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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