Algebraic & Geometric Topology

Chimneys, leopard spots and the identities of Basmajian and Bridgeman

Danny Calegari

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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 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.

Article information

Algebr. Geom. Topol., Volume 10, Number 3 (2010), 1857-1863.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 11J06: Markov and Lagrange spectra and generalizations

orthospectrum identity chimney leopard spot dilogarithm


Calegari, Danny. Chimneys, leopard spots and the identities of Basmajian and Bridgeman. Algebr. Geom. Topol. 10 (2010), no. 3, 1857--1863. doi:10.2140/agt.2010.10.1857.

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