Vol. 266, No. 2, 2013

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The minimal volume orientable hyperbolic 3-manifold with 4 cusps

Ken’ichi Yoshida

Vol. 266 (2013), No. 2, 457–476
Abstract

We prove that the 824 link complement is the minimal volume orientable hyperbolic manifold with 4 cusps. Its volume is twice the volume V 8 of the ideal regular octahedron; that is, 7.32 = 2V 8. The proof relies on Agol’s argument used to determine the minimal volume hyperbolic 3-manifolds with 2 cusps. We also need to estimate the volume of a hyperbolic 3-manifold with totally geodesic boundary which contains an essential surface with nonseparating boundary.

Keywords
hyperbolic 3-manifold, essential surface, geodesic boundary
Mathematical Subject Classification 2010
Primary: 57M27
Milestones
Received: 7 September 2012
Revised: 24 January 2013
Accepted: 4 February 2013
Published: 12 November 2013
Authors
Ken’ichi Yoshida
Graduate School of Mathematical Sciences
University of Tokyo
Tokyo 153-8914
Japan