The collapsibility of CAT(0) square 2-complexes
Ioana-Claudia Laz\u{a}r
TL;DR
This paper establishes a sufficient condition under which finite CAT(0) square 2-complexes can be collapsed to a point, demonstrating their retractability through CAT(0) subspaces.
Contribution
It introduces a new criterion for collapsibility of finite CAT(0) square 2-complexes and proves their retractability via CAT(0) subspaces.
Findings
Finite CAT(0) square 2-complexes retract to a point.
A sufficient condition for collapsibility is provided.
CAT(0) subspaces facilitate the collapse process.
Abstract
We give a sufficient condition for the collapsibility of finite square 2-complexes. We show that any finite, CAT(0) square 2-complex retracts to a point through CAT(0) subspaces.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology