Markoff triples and quasifuchsian groups
Markoff triples and quasifuchsian groups
We study the global behaviour of trees of Markoff triples over the complex numbers. We relate this to the space of type-preserving representations of the punctured torus group into PSL(2, C). In particular, we explore which Markoff triples correspond to quasifuchsian representations. We derive a variation of McShane's identity for quasifuchsian groups. In the case of non-discrete representations, we attempt to relate the asymptotic behaviour of Markoff triples to the realisability of laminations in hyperbolic 3-space. We also consider how some of these issues might be related for more general surfaces.
markoff triple, quasifuchsian group, punctured torus, representation space, lamination
697-736
Bowditch, B.H.
8f3cf0c9-0a10-4b70-8648-33fb2ade7ac9
1998
Bowditch, B.H.
8f3cf0c9-0a10-4b70-8648-33fb2ade7ac9
Bowditch, B.H.
(1998)
Markoff triples and quasifuchsian groups.
Proceedings of the London Mathematical Society, 77, .
(doi:10.1112/S0024611598000604).
Abstract
We study the global behaviour of trees of Markoff triples over the complex numbers. We relate this to the space of type-preserving representations of the punctured torus group into PSL(2, C). In particular, we explore which Markoff triples correspond to quasifuchsian representations. We derive a variation of McShane's identity for quasifuchsian groups. In the case of non-discrete representations, we attempt to relate the asymptotic behaviour of Markoff triples to the realisability of laminations in hyperbolic 3-space. We also consider how some of these issues might be related for more general surfaces.
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Published date: 1998
Keywords:
markoff triple, quasifuchsian group, punctured torus, representation space, lamination
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Local EPrints ID: 29761
URI: http://eprints.soton.ac.uk/id/eprint/29761
ISSN: 0024-6115
PURE UUID: a146c48f-b876-490d-9a52-bafcd149df16
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Date deposited: 14 Mar 2007
Last modified: 15 Mar 2024 07:34
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Author:
B.H. Bowditch
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