Tight complexes are Golod

TL;DR

This paper proves that tight simplicial complexes are Golod, establishing a key link between combinatorial tightness and algebraic Golodness, and shows their equivalence in triangulations of closed orientable manifolds.

Contribution

It demonstrates that tight complexes are Golod and establishes the equivalence of Golodness and tightness for certain manifold triangulations.

Findings

Tight complexes are Golod.

Golodness and tightness are equivalent for triangulations of closed connected orientable manifolds.

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.