The SL(2,C) character variety of the one-holed torus

dc.creatorTan, Ser Peow
dc.creatorWong, Yan Loi
dc.creatorZhang, Ying
dc.date2005-09-02
dc.date.accessioned2026-07-07T06:30:03Z
dc.date.available2026-07-07T06:30:03Z
dc.descriptionIn this note we announce several results concerning the SL(2,C) character variety ${\mathcal X}$ of the one-holed torus. We give a description of the largest open subset ${\mathcal X}_{BQ}$ of ${\mathcal X}$ on which the mapping class group $Γ$ acts properly discontinuously, in terms of two very simple conditions, and show that a series identity generalizing McShane's identity for the punctured torus holds for all characters in this subset. We also give variations of the McShane-Bowditch identities to characters fixed by an Anosov element of $Γ$ with applications to closed hyperbolic three manifolds. Finally we give a definition of end invariants for SL(2,C) characters and give a partial classification of the set of end invariants of a character in ${\mathcal X}$.
dc.description8 pages, announcement
dc.identifierhttps://arxiv.org/abs/math/0509033
dc.identifierhttp://arxiv.org/abs/math/0509033
dc.identifierElectron. Res. Announc. Amer. Math. Soc. 11 (2005) 103-110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98249
dc.subjectGeometric Topology
dc.subjectGroup Theory
dc.subject32G15; 57M50; 30F60
dc.titleThe SL(2,C) character variety of the one-holed torus
dc.typetext

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