Markoff triples and quasifuchsian groups |
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Authors: | Bowditch BH |
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Institution: | Faculty of Mathematical Studies, University of Southampton Highfield, Southampton SO17 1BJ, UK. E-mail: bhb{at}maths.soton.ac.uk |
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Abstract: | We study the global behaviour of trees of Markoff triples overthe complex numbers. We relate this to the space of type-preservingrepresentations of the punctured torus group into SL(2,C). Inparticular, we explore which Markoff triples correspond to quasifuchsianrepresentations. We derive a variation of McShane's identityfor quasifuchsian groups. In the case of non-discrete representations,we attempt to relate the asymptotic behaviour of Markoff triplesto the realisability of laminations in hyperbolic 3-space. Wealso consider how some of these issues might be related formore general surfaces. 1991 Mathematics Subject Classification:57M50. |
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Keywords: | Markoff triple quasifuchsian group punctured torus representation space lamination |
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