Geodesic
The 𝑆𝐿(2,ℂ) character variety of a one-holed torus
Tan, Ser1 ; Wong, Yan1 ; Zhang, Ying1, 2
1 Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
2 Department of Mathematics, Yangzhou University, Yangzhou 225002, P. R. China
Electronic research announcements of the American Mathematical Society, Tome 11 (2005), pp. 103-110 Cet article a éte moissonné depuis la source American Mathematical Society

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In this note we announce several results concerning the ${\mathrm {SL}(2,{\mathbb C})}$ character variety ${\mathcal X}$ of a one-holed torus. We give a description of the largest open subset ${\mathcal X}_{BQ}$ of ${\mathcal X}$ on which the mapping class group $\Gamma$ 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 $\Gamma$ with applications to closed hyperbolic three-manifolds. Finally we give a definition of end invariants for ${\mathrm {SL}(2,{\mathbb C})}$ characters and give a partial classification of the set of end invariants of a character in ${\mathcal X}$.
DOI : 10.1090/S1079-6762-05-00153-8

Tan, Ser 1 ; Wong, Yan 1 ; Zhang, Ying 1, 2

1 Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543
2 Department of Mathematics, Yangzhou University, Yangzhou 225002, P. R. China 
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Tan, Ser; Wong, Yan; Zhang, Ying. The 𝑆𝐿(2,ℂ) character variety of a one-holed torus. Electronic research announcements of the American Mathematical Society, Tome 11 (2005), pp. 103-110. doi: 10.1090/S1079-6762-05-00153-8

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