#### Volume 13, issue 6 (2013)

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Equidecomposability, volume formulae and orthospectra

### Hidetoshi Masai and Greg McShane

Algebraic & Geometric Topology 13 (2013) 3135–3152
##### Abstract

Bridgeman–Kahn and Calegari derived formulae for the volumes of compact hyperbolic $n$–manifolds with totally geodesic boundary in terms of the orthospectrum. Their methods are apparently different from each other, and involve computing the volume of different subspaces of unit tangent bundle of hyperbolic $n$–space. In this paper, we show that the two volume formulae coincide. We also derive a closed form of the formula in dimension 3.

##### Keywords
hyperbolic manifold, volume, orthospectrum
Primary: 57M50
Secondary: 32Q45