Sublinearly Morse geodesics in CAT(0) spaces: lower divergence and hyperplane characterization

Devin Murray; Yulan Qing; Abdul Zalloum

doi:10.2140/agt.2022.22.1337

Sublinearly Morse geodesics in CAT(0) spaces: lower divergence and hyperplane characterization

Devin Murray
, Yulan Qing
, Abdul Zalloum

University of Hawai'i at Mānoa
Fudan University
Queen's University Kingston

Research output: Contribution to journal › Article › peer-review

7 Scopus citations

Abstract

We introduce the notion of k–lower divergence for geodesic rays in CAT(0) spaces. Building on work of Charney and Sultan, we give various characterizations of k– contracting geodesic rays using k–lower divergence and k–slim triangles. We also characterize k–contracting geodesic rays in CAT(0) cube complexes using sequences of well-separated hyperplanes.

Original language	English
Pages (from-to)	1337-1374
Number of pages	38
Journal	Algebraic and Geometric Topology
Volume	22
Issue number	3
DOIs	https://doi.org/10.2140/agt.2022.22.1337
State	Published - 25 Aug 2022
Externally published	Yes

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title = "Sublinearly Morse geodesics in CAT(0) spaces: lower divergence and hyperplane characterization",

abstract = "We introduce the notion of k{\textendash}lower divergence for geodesic rays in CAT(0) spaces. Building on work of Charney and Sultan, we give various characterizations of k{\textendash} contracting geodesic rays using k{\textendash}lower divergence and k{\textendash}slim triangles. We also characterize k{\textendash}contracting geodesic rays in CAT(0) cube complexes using sequences of well-separated hyperplanes.",

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AB - We introduce the notion of k–lower divergence for geodesic rays in CAT(0) spaces. Building on work of Charney and Sultan, we give various characterizations of k– contracting geodesic rays using k–lower divergence and k–slim triangles. We also characterize k–contracting geodesic rays in CAT(0) cube complexes using sequences of well-separated hyperplanes.

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Sublinearly Morse geodesics in CAT(0) spaces: lower divergence and hyperplane characterization

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