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Boundaries for CAT(0) groups

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Iniotakis, Jan-Mark (2003) Boundaries for CAT(0) groups. PhD thesis, University of Warwick.

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Official URL: http://webcat.warwick.ac.uk/record=b3184148~S15

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Abstract

In this thesis we construct a boundary δG for an arbitrary CAT(0) group G. This boundary is compact and invariant under group isomorphisms. It carries a canonical (possibly trivial) G-action by homeomorphisms. For each geometric action of G on a CAT(0) space X there exists a canonical G-equivariant continuous map T : δG → δX. If G is a word-hyperbolic CAT(0) group, its boundary δG coincides with the usual Gromov boundary. If G is free abelian of rank k, its boundary is homeomorphic to the sphere Sk-1. For product groups of the types G X Zk and G x H, where G and H are non-elementary word-hyperbolic CAT(0) groups, the boundary is worked out explicitly. Finally, we prove that the marked length spectrum associated to a geometric action of a torsion-free word-hyperbolic group on a CAT(0) space determines the isometry type of the CAT(0) space up to an additive constant.

Item Type: Thesis or Dissertation (PhD)
Subjects: Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH): Hyperbolic groups, Hyperbolic spaces
Official Date: June 2003
Dates:
DateEvent
June 2003Submitted
Institution: University of Warwick
Theses Department: Mathematics Institute
Thesis Type: PhD
Publication Status: Unpublished
Supervisor(s)/Advisor: Epstein, D. B. A.
Sponsors: Deutscher Akademischer Austauschdienst ; Studienstiftung des Deutschen Volkes ; Engineering and Physical Sciences Research Council
Format of File: pdf
Extent: v, 111 leaves : illustrations
Language: eng

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