Volume 18, issue 6 (2018)

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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 $R=S∕I$ be a monomial ring whose minimal free resolution $F$ is rooted. We describe an ${A}_{\infty }$–algebra structure on $F\phantom{\rule{0.3em}{0ex}}$. Using this structure, we show that $R$ is Golod if and only if the product on ${Tor}^{S}\left(R,k\right)$ 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