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See detailA new identity for SL(2,C)-characters of the once punctured torus group
Hu, Hengnan UL; Tan, Ser Peow; Zhang, Ying

in Mathematical Research Letters (2015), 22(2), 485499

We obtain new variations of the original McShane identity for those SL(2,C)–representations of the once punctured torus group which satisfy the Bowditch conditions, and also for those fixed up to ... [more ▼]

We obtain new variations of the original McShane identity for those SL(2,C)–representations of the once punctured torus group which satisfy the Bowditch conditions, and also for those fixed up to conjugacy by an Anosov mapping class of the torus and satisfying the relative Bowditch conditions. [less ▲]

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See detailNew identities for small hyperbolic surfaces
Hu, Hengnan UL; Tan, Ser Peow

in Bulletin of the London Mathematical Society (2014), 46(5), 10211031

Luo and Tan gave a new identity for hyperbolic surfaces with/without geodesic boundary in terms of dilogarithms of the lengths of simple closed geodesics on embedded three-holed spheres or one-holed tori ... [more ▼]

Luo and Tan gave a new identity for hyperbolic surfaces with/without geodesic boundary in terms of dilogarithms of the lengths of simple closed geodesics on embedded three-holed spheres or one-holed tori in Luo and Tan [‘A dilogarithm identity on moduli spaces of curves’, J. Differential Geom., Preprint, 2011, arXiv:1102.2133[math.GT]]. However, the identity was trivial for a hyperbolic one-holed torus with geodesic boundary. In this paper, we adapt the argument from Luo and Tan to give an identity for hyperbolic tori with one geodesic boundary or cusp in terms of dilogarithm functions on the set of lengths of simple closed geodesics on the torus. As a corollary, we are also able to express the Luo–Tan identity as a sum over all immersed three-holed spheres P which are embeddings when restricted to the interior of P [less ▲]

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