The collapsibility of CAT(0) square $2$-complexes

Ioana-Claudia Lazăr

2020/97/1-2 (1) — DOI: 10.5486/PMD.2020.8619 — pp. 1-25

The collapsibility of CAT(0) square $2$-complexes

Authors: Ioana-Claudia Lazăr

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.

Keywords: square 2-complex, CAT(0) metric, elementary collapse, geodesic segment

Mathematics Subject Classification: 05C99, 05C75, 05E45, 53C23