The collapsibility of some CAT(0) simplicial complexes of dimension 3

TL;DR

This paper investigates the conditions under which certain 3-dimensional CAT(0) simplicial complexes can be collapsed to a point while preserving the CAT(0) property, revealing new collapsibility criteria.

Contribution

It establishes that, under an additional hypothesis, finite CAT(0) simplicial 3-complexes can be collapsed to a point through CAT(0) subspaces, advancing understanding of their topological structure.

Findings

Finite CAT(0) 3-complexes can collapse to a point under specific conditions.

Collapse process preserves the CAT(0) metric at each step.

Provides new criteria for collapsibility of 3-dimensional CAT(0) complexes.

Abstract

We study the collapsibility of finite simplicial complexes of dimension 3 endowed with a CAT(0) metric. Our main result states that, under an additional hypothesis, finite simplicial 3-complexes endowed with a CAT(0) metric collapse to a point through CAT(0) subspaces.