Generalized Markoff Maps and McShane's Identity

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dc.creatorTan, Ser Peow
dc.creatorWong, Yan Loi
dc.creatorZhang, Ying
dc.date2005-02-22
dc.date.accessioned2026-07-07T08:44:04Z
dc.date.available2026-07-07T08:44:04Z
dc.descriptionWe study general representations of the free group on two generators into $SL(2,C)$, and the connection with generalized Markoff maps, following Bowditch. We show that Bowditch's Q-conditions for generalized Markoff maps are sufficient for the generalized McShane identity to hold for the corresponding representations and that the subset of representations satisfying these conditions is the largest open subset in the relative character variety on which the mapping class group acts properly discontinuously. Moreover we generalize Bowditch's results on variations of McShane's identity for complete, finite volume hyperbolic 3-manifolds which fiber over the circle, with the fiber a punctured-torus, to identities for incomplete hyperbolic structures on such manifolds, hence obtaining identities for closed hyperbolic 3-manifolds which are obtained by doing hyperbolic Dehn surgery on such manifolds.
dc.description49 pages, 9 figures
dc.identifierhttps://arxiv.org/abs/math/0502464
dc.identifierhttp://arxiv.org/abs/math/0502464
dc.identifierAdvances in Mathematics 217:2 (2008) 761-813
dc.identifierdoi:10.1016/j.aim.2007.09.004
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142532
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.subject32G15;57M50;30F60
dc.titleGeneralized Markoff Maps and McShane's Identity
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