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