Volume 22, issue 3 (2022)

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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

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.

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boundary, CAT(0) cube complex, sublinearly Morse
Mathematical Subject Classification
Primary: 57M60
Received: 4 October 2020
Revised: 5 April 2021
Accepted: 5 July 2021
Published: 25 August 2022
Devin Murray
Department of Mathematics
University of Hawaii at Manoa
Honolulu, HI
United States
Yulan Qing
Shanghai Center for Mathematical Sciences
Fudan University
Abdul Zalloum
Department of Mathematics and Statistics
Queen’s University
Kinston, ON