A∞–resolutions and the Golod property for monomial rings

Frankhuizen, Robin

doi:10.2140/agt.2018.18.3403

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

Robin Frankhuizen

Algebraic & Geometric Topology 18 (2018) 3403–3424

DOI: 10.2140/agt.2018.18.3403

Abstract

Let $R = S ∕ I$ be a monomial ring whose minimal free resolution $F$ is rooted. We describe an $A_{\infty}$ –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.

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

Volume 18, issue 6 (2018)