Volume 13, issue 6 (2013)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 32Q45
References
Publication
Received: 8 April 2013
Revised: 2 May 2013
Accepted: 7 May 2013
Published: 11 September 2013
Authors
Hidetoshi Masai
Department of Mathematical and Computing Sciences
Tokyo Institute of Technology
O-okayama, Meguro-ku
Tokyo 152-8552
Japan
Greg McShane
Institut Fourier
100 rue des maths, BP 74
38402 St Martin d’Hères
France
http://www-fourier.ujf-grenoble.fr/~mcshane/