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

Murray, Devin; Qing, Yulan; Zalloum, Abdul

doi:10.2140/agt.2022.22.1337

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

Devin Murray, Yulan Qing and Abdul Zalloum

Algebraic & Geometric Topology 22 (2022) 1337–1374

DOI: 10.2140/agt.2022.22.1337

Abstract

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

Keywords

boundary, CAT(0) cube complex, sublinearly Morse

Mathematical Subject Classification

Primary: 57M60

References

Publication

Received: 4 October 2020

Revised: 5 April 2021

Accepted: 5 July 2021

Published: 25 August 2022

Authors

Devin Murray
Department of Mathematics University of Hawaii at Manoa Honolulu, HI United States

Yulan Qing
Shanghai Center for Mathematical Sciences Fudan University Shanghai China

Abdul Zalloum
Department of Mathematics and Statistics Queen’s University Kinston, ON Canada

Volume 22, issue 3 (2022)