A metrizable topology on the contracting boundary of a group

Christopher H. Cashen; John M. Mackay

doi:10.1090/tran/7544

A metrizable topology on the contracting boundary of a group

Christopher H. Cashen, John M. Mackay

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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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.

Original language	English
Pages (from-to)	1555-1600
Number of pages	46
Journal	Transactions of the American Mathematical Society
Volume	372
Issue number	3
Early online date	7 May 2019
DOIs	https://doi.org/10.1090/tran/7544
Publication status	Published - 1 Aug 2019

Keywords

contracting boundary
Morse boundary
boundary at infinity
contracting geodesic
divagation

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10.1090/tran/7544

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via American Mathematical Society at http://www.ams.org/journals/tran/0000-000-00/S0002-9947-2019-07544-X/ . Please refer to any applicable terms of use of the publisher.
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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. ",

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AB - 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.

KW - contracting boundary

KW - Morse boundary

KW - boundary at infinity

KW - contracting geodesic

KW - divagation

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A metrizable topology on the contracting boundary of a group

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Optimal geometric structures for hyperbolic groups

Dr John M Mackay

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A metrizable topology on the contracting boundary of a group

Abstract

Keywords

Access to Document

Handle.net

Other files and links

Fingerprint

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Optimal geometric structures for hyperbolic groups

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Dr John M Mackay

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