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Ian Agol

Geometry & Topology 6 (2002) 905–916

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 > .32.

Keywords
hyperbolic structure, 3–manifold, volume, geodesic
Mathematical Subject Classification 2000
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
Authors
Ian Agol
MSCS
SEO 322
m/c 249
University of Illinois at Chicago
851 S Morgan St
Chicago
Illinois 60607-7045
USA
http://www.math.uic.edu/~agol/