The minimal volume orientable hyperbolic 2-cusped 3-manifolds

@article{Agol2010TheMV,
  title={The minimal volume orientable hyperbolic 2-cusped 3-manifolds},
  author={I. Agol},
  journal={arXiv: Geometric Topology},
  year={2010},
  volume={138},
  pages={3723-3732}
}
  • I. Agol
  • Published 2010
  • Mathematics
  • arXiv: Geometric Topology
We prove that the Whitehead link complement and the pretzel link complement are the minimal volume orientable hyperbolic 3-manifolds with two cusps, with volume = 4 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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