English

Tight complexes are Golod

Algebraic Topology 2023-09-06 v2 Commutative Algebra Combinatorics

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.

Keywords

Cite

@article{arxiv.2302.02532,
  title  = {Tight complexes are Golod},
  author = {Kouyemon Iriye and Daisuke Kishimoto},
  journal= {arXiv preprint arXiv:2302.02532},
  year   = {2023}
}

Comments

17 pages, minor corrections

R2 v1 2026-06-28T08:32:36.066Z