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arXiv · 1005.4858

Chimneys, leopard spots, and the identities of Basmajian and Bridgeman

Danny Calegari
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Abstract

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) = \sum_i q_n(e^{l_i}) where the sum is taken over the orthospectrum of M. When n=3, this has the explicit form \sum_i 1/(e^{2l_i}-1) = -χ(S)/4.

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Danny Calegari. 2010-07-27. Chimneys, leopard spots, and the identities of Basmajian and Bridgeman. https://doi.org/10.2140/agt.2010.10.1857

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