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Stability and the Morse boundary

Abstract:

Stable subgroups and the Morse boundary are two systematic approaches to collect and study the hyperbolic aspects of finitely generated groups. In this paper we unify and generalise these strategies by viewing any geodesic metric space as a countable union of stable subspaces: we show that every stable subgroup is a quasi-convex subset of a set in this collection and that the Morse boundary is recovered as the direct limit of the usual Gromov boundaries of these hyperbolic subspaces.

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/jlms.12042

Authors


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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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Funding agency for:
Cordes, M
Grant:
DMS-1106726
More from this funder
Funding agency for:
Hume, D
Grant:
ANR-14-CE25-0004
Publisher:
Wiley Publisher's website
Journal:
Journal of the London Mathematical Society Journal website
Publication date:
2017-03-28
Acceptance date:
2017-02-21
DOI:
EISSN:
1469-7750
ISSN:
0024-6107
Source identifiers:
692470
Keywords:
Pubs id:
pubs:692470
UUID:
uuid:fc79152e-9d3f-4533-a6fe-4c9f520573e9
Local pid:
pubs:692470
Deposit date:
2017-05-05

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