Calegari, Danny (2010) Chimneys, leopard spots and the identities of Basmajian and Bridgeman. Algebraic and Geometric Topology, 10 (3). pp. 1857-1863. ISSN 1472-2747 http://resolver.caltech.edu/CaltechAUTHORS:20101122-112850841
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We give a simple geometric argument to derive in a common manner orthospectrum identities of Basmajian and Bridgeman. Our method also considerably simplifies the determination of the summands in these identities. For example, for every odd integer n, there is a rational function q_n of degree 2(n − 2) so that if M is a compact hyperbolic manifold of dimension n with totally geodesic boundary S, there is an identity χ(S) = ∑_(i) q_(n)(e^l_i) where the sum is taken over the orthospectrum of M. When n = 3, this has the explicit form ∑_(i) 1/(e^(2l_(i)) − 1) = −χ(S)/4.
|Additional Information:||© 2010 Mathematical Sciences Publishers. Received: 26 May 2010, Revised: 26 July 2010, Accepted: 28 July 2010, Published: 3 September 2010. I would like to thank Martin Bridgeman, Jeremy Kahn, Sadayoshi Kojima, Greg McShane and Maryam Mirzakhani for some useful discussions. In particular, this paper owes an obvious debt to  and the beautiful sequel . Thanks also to the referee for a useful correction. The first version of this paper was written before the author was aware of , and I am very grateful to Greg and Sadayoshi for bringing it to my attention. The author was supported by NSF grant DMS 0707130.|
|Classification Code:||Primary 57M50; Secondary 11J06|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Benjamin Perez|
|Deposited On:||22 Nov 2010 23:43|
|Last Modified:||26 Dec 2012 12:40|
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