The minimal volume orientable hyperbolic 2-cusped 3-manifolds

Details The minimal volume orientable hyperbolic 2-cusped 3-manifolds The minimal volume orientable hyperbolic 2-cusped 3-manifolds

2008-03-31

arxiv.org/abs/0804.0043v2

electronically published May 12, 2010, Proc. Amer. Math. Soc. (2010), http://www.ams.org/journals/proc/0000-000-00/S0002-993

Mathematics

Geometric Topology

10 pages, 5 figures, incorporated referees comments, includes hyperref links

Scientific paper

10.1090/S0002-9939-10-10364-5

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 x 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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