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• W2269280016 abstract "We present a monomial ideal $mathfrak{a} subset S$ such that $S/mathfrak{a}$ is not Golod, even though the product on its Koszul homology is trivial. This constitutes a counterexample to a well-known result by Berglund and Jollenbeck (the error can be traced to a mistake in an earlier article by Jollenbeck). On the positive side, we show that if $R$ is a monomial ring such that the $r$-ary Massey product vanish for all $r leq max(2, mathrm{reg} R-2)$, then $R$ is Golod. In particular, if $R$ is the Stanley-Reisner ring of a simplicial complex of dimension at most $3$, then $R$ is Golod if and only if the product on its Koszul homology is trivial. Moreover, we show that if $Delta$ is a triangulation of a $Bbbk$-orientable manifold whose Stanley-Reisner ring is Golod, then $Delta$ is $2$-neighborly. This extends a recent result of Iriye and Kishimoto." @default.
• W2269280016 created "2016-06-24" @default.
• W2269280016 creator A5032425086 @default.
• W2269280016 date "2015-11-16" @default.
• W2269280016 modified "2023-09-27" @default.
• W2269280016 title "A non-Golod ring with a trivial product on its Koszul homology" @default.
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