McShane's identity
In geometric topology, McShane's identity for a once punctured torus T {\displaystyle \mathbb {T} } with a complete, finite-volume hyperbolic structure is given by ∑ γ 1 1 + e ℓ ( γ ) = 1 2 {\displaystyle \sum _{\gamma }{\frac {1}{1+e^{\ell (\gamma )}}}={\frac {1}{2}}} where the sum is over all (unoriented) simple closed geodesics γ on the torus; and ℓ(γ) denotes the hyperbolic length of γ. This identity was generalized by Maryam Mirzakhani in her PhD thesis == References == == Further reading == Tan, Ser Peow; Wong, Yan Loi; Zhang, Ying (April 2006).