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2010 Chimneys, leopard spots and the identities of Basmajian and Bridgeman
Danny Calegari
Algebr. Geom. Topol. 10(3): 1857-1863 (2010). DOI: 10.2140/agt.2010.10.1857

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 qn of degree 2(n2) so that if M is a compact hyperbolic manifold of dimension n with totally geodesic boundary S, there is an identity χ(S)=iqn(eli) where the sum is taken over the orthospectrum of M. When n=3, this has the explicit form i1(e2li1)=χ(S)4.

Citation

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Danny Calegari. "Chimneys, leopard spots and the identities of Basmajian and Bridgeman." Algebr. Geom. Topol. 10 (3) 1857 - 1863, 2010. https://doi.org/10.2140/agt.2010.10.1857

Information

Received: 26 May 2010; Revised: 26 July 2010; Accepted: 28 July 2010; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1196.57010
MathSciNet: MR2684984
Digital Object Identifier: 10.2140/agt.2010.10.1857

Subjects:
Primary: 57M50
Secondary: 11J06

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.10 • No. 3 • 2010
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