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4 - A survey on Morse boundaries and stability

from Part Two - Expository Articles

Published online by Cambridge University Press:  22 June 2019

Edited by
Mark Hagen ,
Richard Webb  and
Henry Wilton
Mark Hagen
Affiliation:
University of Bristol
Richard Webb
Affiliation:
University of Cambridge
Henry Wilton
Affiliation:
University of Cambridge
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Summary

The goal of this survey is to define and explain the Morse boundary of a geodesic space, a generalisation of the Gromov boundary of a hyperbolic space that records the “hyperbolic directions” in the space.This article relates Morse boundaries to the notion of stability, which generalises to arbitrary geodesic spaces the notion of quasiconvexity in hyperbolic spaces.

Keywords

Morse geodesiccontracting geodesicMorse boundarycontracting boundaryGromov boundarydirect limit topologystable subspacequasiconvex subspacecapacity dimensionasymptotic dimensionstable equivalencemapping class groupright-angled Artin groupBowditch boundaryconvex-cocompact
Type
Chapter
Information
Beyond Hyperbolicity , pp. 83 - 116
Publisher: Cambridge University Press
Print publication year: 2019

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