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.
References
- Necessary and Sufficient Conditions for McShane's Identity and Variations Ser Peow Tan, Yan Loi Wong, and Ying Zhang eprint arXiv:math/0411184
- McShane, G. Simple geodesics and a series constant over Teichmuller space. Invent. Math. 132 (1998), no. 3, 607–632.
This article is issued from Wikipedia - version of the 2/1/2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.