A survey of length series identities for surfaces, % 3-manifolds and representation varieties

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dc.creatorTan, Ser Peow
dc.creatorWong, Yan Loi
dc.creatorZhang, Ying
dc.date2006-07-05
dc.date.accessioned2026-07-07T07:37:26Z
dc.date.available2026-07-07T07:37:26Z
dc.descriptionWe survey some of our recent results on length series identities for hyperbolic (cone) surfaces, possibly with cusps and/or boundary geodesics; classical Schottky groups; representations/characters of the one-holed torus group to $SL(2, \mathbf C)$; and hyperbolic 3 manifolds obtained by hyperbolic Dehn surgery on punctured torus bundles over the circle. These can be regarded as generalizations and variations of McShane's identity for cusped hyperbolic surfaces, which has found some striking applications in the recent work of Mirzakhani. We discuss some of the methods and techniques used to obtain these identities.
dc.description22 pages, submitted to proceedings of symposium "Complex Analysis and Geometry of Hyperbolic Spaces", Dec 2005, RIMS, Kyoto, Japan
dc.identifierhttps://arxiv.org/abs/math/0607107
dc.identifierhttp://arxiv.org/abs/math/0607107
dc.identifierRIMS Kokyuroku 1518, October 2006, pp. 20-41.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/120778
dc.subjectGeometric Topology
dc.subjectDifferential Geometry
dc.subject32G15;57M50;30F60
dc.titleA survey of length series identities for surfaces, % 3-manifolds and representation varieties
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