On r-stacked triangulated manifolds

TL;DR

This paper extends the concept of r-stackedness from simplicial polytopes to triangulated homology manifolds, exploring their properties and establishing a new necessary condition for their face vectors under certain conditions.

Contribution

It introduces r-stackedness for triangulated homology manifolds and derives a new necessary condition for their face vectors when vertex links are polytopal.

Findings

Defined r-stackedness for triangulated homology manifolds.

Studied basic properties of r-stacked manifolds.

Established a new necessary condition for face vectors.

Abstract

The notion of r-stackedness for simplicial polytopes was introduced by McMullen and Walkup in 1971 as a generalization of stacked polytopes. In this paper, we define the r-stackedness for triangulated homology manifolds and study their basic properties. In addition, we find a new necessary condition for face vectors of triangulated manifolds when all the vertex links are polytopal.