A metrizable topology on the contracting boundary of a group
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- by Christopher H. Cashen and John M. Mackay PDF
- Trans. Amer. Math. Soc. 372 (2019), 1555-1600 Request permission
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.References
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Additional Information
- Christopher H. Cashen
- Affiliation: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
- MR Author ID: 902549
- John M. Mackay
- Affiliation: School of Mathematics, University of Bristol, Bristol, United Kingdom
- MR Author ID: 845756
- Received by editor(s): August 18, 2017
- Received by editor(s) in revised form: February 13, 2018
- Published electronically: May 7, 2019
- Additional Notes: The first author thanks the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the program Non-positive curvature: group actions and cohomology where work on this paper was undertaken. This work was partially supported by EPSRC Grant Number EP/K032208/1 and by the Austrian Science Fund (FWF): P30487-N35.
The second author was supported in part by the National Science Foundation under Grant DMS-1440140 while visiting the Mathematical Sciences Research Institute in Berkeley, California, during the Fall 2016 semester, and in part by EPSRC grant EP/P010245/1. - © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 1555-1600
- MSC (2010): Primary 20F65, 20F67
- DOI: https://doi.org/10.1090/tran/7544
- MathSciNet review: 3976570