Algebraic & Geometric Topology

Chimneys, leopard spots and the identities of Basmajian and Bridgeman

Danny Calegari

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 $2(n−2)$ so that if $M$ is a compact hyperbolic manifold of dimension $n$ with totally geodesic boundary $S$, there is an identity $χ(S)= ∑iqn(eli)$ where the sum is taken over the orthospectrum of $M$. When $n=3$, this has the explicit form $∑i1∕(e2li−1)=−χ(S)∕4$.

Article information

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

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

https://projecteuclid.org/euclid.agt/1513715155

Digital Object Identifier
doi:10.2140/agt.2010.10.1857

Mathematical Reviews number (MathSciNet)
MR2684984

Zentralblatt MATH identifier
1196.57010

Citation

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. https://projecteuclid.org/euclid.agt/1513715155

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