The notions Golodness and tightness for simplicial complexes come from algebra and geometry, respectively. We prove these two notions are equivalent for 3-manifold triangulations, through a topological characterization of a polyhedral product for a tightneighborly manifold triangulation of dimension ≥ 3.

Abstract Golodness of two-dimensional simplicial complexes is studied through polyhedral products, and combinatorial and topological characterizations of Golodness of surface triangulations are… Expand

Let K be a simplicial complex such that the Taylor resolution for its Stanley-Reisner ring is minimal. We prove that the following conditions are equivalent: (1) K is Golod; (2) any two minimal… Expand

A computer-friendly combinatorial scheme to obtain tight triangulations and new examples in dimensions three, four, and five are presented and shown that there are abundantly many.Expand

Two results are proved on stacked triangulated manifolds: if $\Delta$ is a tight connected closed homology $d$-manifold whosei$th homology vanishes for $1 < i < d-1$, then $\Delta $ is a stacked triangling of a manifold.Expand

Immersions or maps of closed manifolds in Euclidean space, of minimal absolute total curvature are called tight in this paper. (They were called convex in [25].) After the definition in Chapter 1,… Expand