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|Title:||The SL(2, ℂ) character variety of a one-holed torus||Authors:||Tan, S.P.
|Issue Date:||2005||Citation:||Tan, S.P., Wong, Y.L., Zhang, Y. (2005). The SL(2, ℂ) character variety of a one-holed torus. Electronic Research Announcements of the American Mathematical Society 11 : 103-110. ScholarBank@NUS Repository. https://doi.org/10.1090/S1079-6762-05-00153-8||Abstract:||In this note we announce several results concerning the SL(2, ℂ) character variety χ of a one-holed torus. We give a description of the largest open subset χBQ of χ 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 for 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 χ. © 2005 American Mathematical Society.||Source Title:||Electronic Research Announcements of the American Mathematical Society||URI:||http://scholarbank.nus.edu.sg/handle/10635/104355||ISSN:||10796762||DOI:||10.1090/S1079-6762-05-00153-8|
|Appears in Collections:||Staff Publications|
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