Volume change under drilling

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

References

Forward citations

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/

Volume 6, issue 2 (2002)

Ian Agol