Closed subsets of a CAT(0) 2–complex are intrinsically CAT(0)

Ricks, Russell

doi:10.2140/agt.2021.21.1723

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Closed subsets of a $\mathrm{CAT}(0)$ $2$–complex are intrinsically $\mathrm{CAT}(0)$

Russell Ricks

Algebraic & Geometric Topology 21 (2021) 1723–1744

DOI: 10.2140/agt.2021.21.1723

Abstract

Let $κ \leq 0$ , and let $X$ be a complete, locally finite $CAT (κ)$ polyhedral $2$ –complex $X$ , each face with constant curvature $κ$ . Let $E$ be a closed, rectifiably connected subset of $X$ with trivial first singular homology. We show that $E$ , under the induced path metric, is a complete $CAT (κ)$ space.

Keywords

$\mathrm{CAT}(0)$, complex, subspaces

Mathematical Subject Classification 2010

Primary: 51K10

References

Publication

Received: 30 August 2019

Revised: 11 December 2019

Accepted: 21 July 2020

Published: 18 August 2021

Authors

Russell Ricks
Department of Mathematical Sciences Binghamton University Binghamton, NY United States

Volume 21, issue 4 (2021)