On stacked triangulated manifolds

Abstract

We prove two results on stacked triangulated manifolds in this paper: (a) every stacked triangulation of a connected manifold with or without boundary is obtained from a simplex or the boundary of a simplex by certain combinatorial operations; (b) in dimension $d\ge 4$, if $\Delta$ is a tight connected closed homology $d$-manifold whose $i$th homology vanishes for $1<i<d-1$, then $\Delta$ is a stacked triangulation of a manifold.These results give affirmative answers to questions posed by Novik and Swartz and by Effenberger.

11 pages, minor changes in the organization of the paper, add information about recent results

References in corpus (6)

• Separation index of graphs and stacked 2-spheres
• On stellated spheres, shellable balls, lower bounds and a combinatorial criterion for tightness
• On stellated spheres and a tightness criterion for combinatorial manifolds
• On polytopal upper bound spheres
• The mu vector, Morse inequalities and a generalized lower bound theorem for locally tame combinatorial manifolds
• On the generalized lower bound conjecture for polytopes and spheres

Cited by in corpus (3)

• Tight triangulations of closed 3-manifolds
• A characterization of tightly triangulated 3-manifolds
• Tight and stacked triangulations of manifolds