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

Robin Frankhuizen

Algebraic & Geometric Topology 18 (2018) 3403–3424
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.

Keywords
Golod ring, Poincaré series, A-infinity algebra, Massey products
Mathematical Subject Classification 2010
Primary: 13D07, 13D40, 16E45, 55S30
References
Publication
Received: 11 October 2017
Revised: 16 April 2018
Accepted: 16 June 2018
Published: 18 October 2018
Authors
Robin Frankhuizen
School of Mathematics
University of Southampton
Southampton
United Kingdom