McShane's identity

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In geometric topology, McShane's identity for a once punctured torus \mathbb{T} with a complete, finite volume hyperbolic structure is given by

\sum_\gamma \frac{1}{1 + e^{l(\gamma)}}=\frac{1}{2}.

Here γ is a simple closed geodesic on the torus and l(γ) is denotes the hyperbolic length of γ.

[edit] References

  • Necessary and Sufficient Conditions for McShane's Identity and Variations Ser Peow Tan, Yan Loi Wong, and Ying Zhang eprint arXiv:math/0411184 [1]