The minimal volume orientable hyperbolic 3-manifold with 4 cusps

Ken’ichi Yoshida

Vol. 266 (2013), No. 2, 457–476

DOI: 10.2140/pjm.2013.266.457

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