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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

Let κ 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.

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$\mathrm{CAT}(0)$, complex, subspaces
Mathematical Subject Classification 2010
Primary: 51K10
Received: 30 August 2019
Revised: 11 December 2019
Accepted: 21 July 2020
Published: 18 August 2021
Russell Ricks
Department of Mathematical Sciences
Binghamton University
Binghamton, NY
United States