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Quasi-mobius maps between Morse boundaries of CAT(0) spaces

Groups acting on CAT(0) spaces September 27, 2016 - September 30, 2016

September 29, 2016 (09:00 AM PDT - 09:50 AM PDT)
Speaker(s): Ruth Charney (Brandeis University)
Location: MSRI: Simons Auditorium
  • CAT(0) space

  • negative curvature manifolds

  • Riemannian geometry

  • visual boundary

  • Morse boundary

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



The Morse boundary of a geodesic metric space is a topological space consisting of equivalence classes of geodesic rays satisfying a Morse condition.  A key property of this boundary is quasi-isometry invariance:  a quasi-isometry between two proper geodesic metric spaces induces a homeomorphism on their Morse boundaries.  In the case of a hyperbolic metric space, the Morse boundary is the usual Gromov boundary and Paulin proved that this boundary, together with its quasi-mobius structure, determines the space up to quasi-isometry.  I will discuss an analogue of Paulin’s theorem for Morse boundaries of CAT(0) spaces.  This is joint work with Devin Murray.

26816?type=thumb Charney.Notes 842 KB application/pdf Download
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