Geometry & Topology 6 (2002) 905–916

DOI: 10.2140/gt.2002.6.905

arXiv: math.GT/0101138

Abstract

Given a hyperbolic 3–manifold M containing an embedded closed geodesic, we estimate the volume of a complete hyperbolic metric on the complement of the geodesic in terms of the geometry of M. As a corollary, we show that the smallest volume orientable hyperbolic 3–manifold has volume >0.32.

Keywords

hyperbolic structure, 3–manifold, volume, geodesic

Mathematical Subject Classification

Primary: 57M50

Secondary: 53C15, 53C22

References

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Publication

Received: 17 January 2001
Revised: 7 November 2002
Accepted: 31 December 2002
Published: 31 December 2002
Proposed: David Gabai
Seconded: Walter Neumann, John Morgan

Authors