The minimal volume orientable hyperbolic 3-manifold with 4 cusps

Ken'ichi Yoshida

doi:10.2140/pjm.2013.266.457

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arXiv · 1209.1374

The minimal volume orientable hyperbolic 3-manifold with 4 cusps

Ken'ichi Yoshida

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Abstract

We prove that the 8^4_2 link complement is the minimal volume orientable hyperbolic manifold with 4 cusps. Its volume is twice of the volume V_8 of the ideal regular octahedron, i.e. 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 non-separating boundary.

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Ken'ichi Yoshida. 2012-09-06. The minimal volume orientable hyperbolic 3-manifold with 4 cusps. https://doi.org/10.2140/pjm.2013.266.457

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