Equidecomposability, volume formulae and orthospectra

Masai, Hidetoshi; McShane, Greg

doi:10.2140/agt.2013.13.3135

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Equidecomposability, volume formulae and orthospectra

Hidetoshi Masai and Greg McShane

Algebraic & Geometric Topology 13 (2013) 3135–3152

DOI: 10.2140/agt.2013.13.3135

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/

Volume 13, issue 6 (2013)