A Metrizable Topology on the Contracting Boundary of a Group
arXiv:1703.01482 · doi:10.1090/tran/7544
Abstract
The 'contracting boundary' of a proper geodesic metric space consists of equivalence classes of geodesic rays that behave like rays in a hyperbolic space. We introduce a geometrically relevant, quasi-isometry invariant topology on the contracting boundary. When the space is the Cayley graph of a finitely generated group we show that our new topology is metrizable.
v1: 26 pages, 3 figures; v2: 44 pages, 6 figures, additional results; v3: 46 pages, 7 figures, minor changes
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