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Convergence groups and configuration spaces

Convergence groups and configuration spaces
Convergence groups and configuration spaces
We give an account of convergence groups from the point of view of groups which act properly discontinuously on spaces of distinct triples. We give a proof of the equivalence of this characterisation with the dynamical definition of Gehring and Martin. We focus our attention on uniform convergence groups, i.e. those for which the action on the space of distinct triples is also cocompact, and explore some of their properties from a purely dynamical point of view. We show that the space of distinct unordered n-tuples in any continuum is connected. Moreover, the spaces of distinct ordered n-tuples in any metrisable continuum other than a circle or an arc is also connected.
3110163667
23-54
Walter de Gruyter
Bowditch, Brian H.
559a0b03-4ffd-49b0-aafe-4764e7de5143
Cossey, John
Miller III, Charles F.
Neumann, Walter D.
Shapiro, Michael
Bowditch, Brian H.
559a0b03-4ffd-49b0-aafe-4764e7de5143
Cossey, John
Miller III, Charles F.
Neumann, Walter D.
Shapiro, Michael

Bowditch, Brian H. (1999) Convergence groups and configuration spaces. Cossey, John, Miller III, Charles F., Neumann, Walter D. and Shapiro, Michael (eds.) In Geometric Group Theory Down Under: Proceedings of a Special Year in Geometric Group Theory, Canberra, Australia, 1996. Walter de Gruyter. pp. 23-54.

Record type: Conference or Workshop Item (Paper)

Abstract

We give an account of convergence groups from the point of view of groups which act properly discontinuously on spaces of distinct triples. We give a proof of the equivalence of this characterisation with the dynamical definition of Gehring and Martin. We focus our attention on uniform convergence groups, i.e. those for which the action on the space of distinct triples is also cocompact, and explore some of their properties from a purely dynamical point of view. We show that the space of distinct unordered n-tuples in any continuum is connected. Moreover, the spaces of distinct ordered n-tuples in any metrisable continuum other than a circle or an arc is also connected.

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Published date: 1999

Identifiers

Local EPrints ID: 29767
URI: https://eprints.soton.ac.uk/id/eprint/29767
ISBN: 3110163667
PURE UUID: 0b8ce9a0-e2df-4a06-8d35-07a0d089caec

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Date deposited: 18 May 2007
Last modified: 17 Jul 2017 15:57

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