Face vectors of simplicial cell decompositions of manifolds

TL;DR

This paper characterizes the face vectors of simplicial posets corresponding to cell decompositions of topological manifolds, especially focusing on products of spheres and odd-dimensional manifolds, advancing understanding of their combinatorial structures.

Contribution

It provides a complete characterization of face vectors for simplicial posets of manifolds, including products of spheres and odd-dimensional manifolds, filling a gap in topological combinatorics.

Findings

Characterization of face vectors for manifolds homeomorphic to products of spheres

Characterization of face vectors for odd-dimensional manifolds without boundary

New combinatorial criteria for simplicial posets of topological manifolds

Abstract

In this paper, we study face vectors of simplicial posets that are the face posets of cell decompositions of topological manifolds without boundary. We characterize all possible face vectors of simplicial posets whose geometric realizations are homeomorphic to the product of spheres. As a corollary, we obtain the characterization of face vectors of simplicial posets whose geometric realizations are odd dimensional manifolds without boundary.