The minimal volume orientable hyperbolic 2-cusped 3-manifolds

Agol, Ian

doi:10.1090/S0002-9939-10-10364-5

The minimal volume orientable hyperbolic 2-cusped 3-manifolds
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by Ian Agol

Proc. Amer. Math. Soc. 138 (2010), 3723-3732

DOI: https://doi.org/10.1090/S0002-9939-10-10364-5

Published electronically: May 12, 2010

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Erratum: Proc. Amer. Math. Soc. 75 (1979), 375.

Abstract:

We prove that the Whitehead link complement and the $(-2,3,8)$ pretzel link complement are the minimal volume orientable hyperbolic 3-manifolds with two cusps, with volume $3.66...$ = 4 $\times$ Catalan’s constant. We use topological arguments to establish the existence of an essential surface which provides a lower bound on volume and strong constraints on the manifolds that realize that lower bound.

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