Geometric topology

McShane's identity

In geometric topology, McShane's identity for a once punctured torus with a complete, finite-volume hyperbolic structure is given by where * the sum is over all simple closed geodesics γ on the torus; and * ℓ(γ) denotes the hyperbolic length of γ. This identity was generalized by Maryam Mirzakhani on her PhD thesis (Wikipedia).

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Related pages

Geometric topology | Torus | Maryam Mirzakhani