Geometry & Topology, Vol. 6 (2002) Paper no. 27, pages 905--916.

Volume change under drilling

Ian Agol

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

AMS subject classification. Primary: 57M50. Secondary: 53C15, 53C22.

DOI: 10.2140/gt.2002.6.905

E-print: arXiv:math.GT/0101138

Submitted to GT on 17 January 2001. (Revised 7 November 2002.) Paper accepted 31 December 2002. Paper published 31 December 2002.

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Ian Agol
MSCS, SEO 322, m/c 249, University of Illinois at Chicago
851 S Morgan St, Chicago, IL 60607-7045, USA
Email: agol@math.uic.edu
URL: http://www.math.uic.edu/~agol
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