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 (unoriented) simple closed geodesics γ on the torus; and
• ℓ(γ) denotes the hyperbolic length of ÃŽÂ³.

This identity was generalized by Maryam Mirzakhani in her PhD thesis

References

Further reading