Massey products and the Golod property for simplicially resolvable rings

Abstract

We apply algebraic Morse theory to the Taylor resolution of a monomial ring $R=S/I$ to obtain an $A_{\infty }$-structure on the minimal free resolution of $R$. Using this structure we describe the vanishing of higher Massey products in case the minimal free resolution is simplicial. Under this assumption, we show that R is Golod if and only if the product on ${\text{Tor}}^S(R,k)$ vanishes. Lastly, we give two combinatorial characterizations of the Golod property in this case.

27 pages; comments welcome. arXiv admin note: text overlap with arXiv:1612.02737

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