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

Autor:	Russell Ricks
Rok vydání:	2021
Předmět:	Combinatorics Constant curvature Mathematics - Metric Geometry Induced path Face (geometry) Metric (mathematics) FOS: Mathematics Mathematics::Metric Geometry Metric Geometry (math.MG) Geometry and Topology Space (mathematics) Mathematics Singular homology
Zdroj:	Algebraic & Geometric Topology. 21:1723-1744
ISSN:	1472-2739 1472-2747
DOI:	10.2140/agt.2021.21.1723
Popis:	Let k be at most 0, and let X be a locally-finite CAT(k) polyhedral 2-complex X, each face with constant curvature k. 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(k) space. Comment: 13 pages, 3 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::31959eb1ec7ed7e18dda4ff4f42d3d9a https://doi.org/10.2140/agt.2021.21.1723 Zobrazit plný text záznamu