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.

Notes on file formats

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
GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.