Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Search

Refine search

Refine search

Access:
Content type:
Publication date:
Apply   From and To filters
Subject: Show more
Journals Show more
Publishers: Show more
Societies Show more
Series: Show more
Collections: Show more

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

3 results

  • 4 - A survey on Morse boundaries and stability

  • from Part Two - Expository Articles
  • Edited by Mark Hagen, University of Bristol, Richard Webb, University of Cambridge, Henry Wilton, University of Cambridge
  • Book:
    Beyond Hyperbolicity
    Published online:
    22 June 2019
    Print publication:
    11 July 2019, pp 83-116

  • 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.

  • Martin boundaries of the duals of free unitary quantum groups

  • Part of
  • Sara Malacarne, Sergey Neshveyev
  • Journal:
    Compositio Mathematica / Volume 155 / Issue 6 / June 2019
    Published online by Cambridge University Press:
    31 May 2019, pp. 1171-1193
    Print publication:
    June 2019
    • Article
      • You have access
    • PDF
    • HTML
    • Export citation

  • Given a free unitary quantum group $G=A_{u}(F)$, with $F$ not a unitary $2\times 2$ matrix, we show that the Martin boundary of the dual of $G$ with respect to any $G$-${\hat{G}}$-invariant, irreducible, finite-range quantum random walk coincides with the topological boundary defined by Vaes and Vander Vennet. This can be thought of as a quantum analogue of the fact that the Martin boundary of a free group coincides with the space of ends of its Cayley tree.