English

Minimally non-Golod face rings and Massey products

Algebraic Topology 2023-02-14 v1 Commutative Algebra Combinatorics

Abstract

We give a correct statement and a complete proof of the criterion obtained by Grbi\'c, Panov, Theriault and Wu for the face ring k[K]\Bbbk[K] of a simplicial complex KK to be Golod over a field k\Bbbk. (The original argument depended on the main result of a paper by Berglund and J\"ollenbeck, which was shown to be false by Katth\"an.) We also construct an example of a minimally non-Golod complex KK such that the cohomology of the corresponding moment-angle complex ZK\mathcal Z_K has trivial cup product and a non-trivial triple Massey product.

Keywords

Cite

@article{arxiv.2201.12779,
  title  = {Minimally non-Golod face rings and Massey products},
  author = {Ivan Limonchenko and Taras Panov},
  journal= {arXiv preprint arXiv:2201.12779},
  year   = {2023}
}

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3 pages