The Fundamental Group of Balanced Simplicial Complexes and Posets

TL;DR

This paper provides an upper bound on the size of minimal generating sets for the fundamental group of balanced simplicial complexes and posets, advancing understanding of their topological properties.

Contribution

It introduces a new upper bound on the fundamental group's minimal generating set size for a broad class of balanced simplicial complexes and posets.

Findings

Established an upper bound for the fundamental group's minimal generators.

Applied the bound to a large family of balanced simplicial complexes.

Extended results to simplicial posets.

Abstract

We establish an upper bound on the cardinality of a minimal generating set for the fundamental group of a large family of connected, balanced simplicial complexes and, more generally, simplicial posets.