Volume 6, issue 2 (2002)

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Volume change under drilling

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