Quasi-mobius maps between Morse boundaries of CAT(0) spaces
Groups acting on CAT(0) spaces September 27, 2016 - September 30, 2016
Location: SLMath: Eisenbud Auditorium
CAT(0) space
negative curvature manifolds
Riemannian geometry
visual boundary
Morse boundary
54C40 - Algebraic properties of function spaces in general topology [See also 46Exx]
01-11 - Research data for problems pertaining to history and biography
55R35 - Classifying spaces of groups and $H$H-spaces in algebraic topology
55R91 - Equivariant fiber spaces and bundles in algebraic topology [See also 19L47]
55R65 - Generalizations of fiber spaces and bundles in algebraic topology
55S36 - Extension and compression of mappings in algebraic topology
14614
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.
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