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  • Print publication year: 2019
  • Online publication date: June 2019

4 - A survey on Morse boundaries and stability

from Part Two - Expository Articles


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.