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Volume change under drilling
Ian Agol
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Geometry & Topology 6 (2002)
905–916
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Abstract
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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.
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Keywords
hyperbolic structure, 3–manifold,
volume, geodesic
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Mathematical Subject Classification
Primary: 57M50
Secondary: 53C15, 53C22
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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
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