Tight complexes are Golod

Kouyemon Iriye; Daisuke Kishimoto

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arXiv · 2302.02532

Tight complexes are Golod

Kouyemon Iriye·Daisuke Kishimoto

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Abstract

The Golodness of a simplicial complex is defined algebraically in terms of the Stanley-Reisner ring, and it has been a long-standing problem to find its combinatorial characterization. The tightness of a simplicial complex is a combinatorial analogue of a tight embedding of a manifold into the Euclidean space, and has been studied in connection to minimal manifold triangulations. In this paper, we prove that tight complexes are Golod, and as a corollary, we obtain that for triangulations of closed connected orientable manifolds, the Golodness and the tightness are equivalent.

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BibTeX RIS

Kouyemon Iriye, Daisuke Kishimoto. 2023-02-06. Tight complexes are Golod. https://arxiv.org/abs/2302.02532

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