The minimal volume orientable hyperbolic 2-cusped 3-manifolds
By Ian Agol. 2008
60 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/9bd2291b309790dbf5a8dc19bc345f515da34b11
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In Applied Mathematics
In Geometry and Topology
- John William Aaber
- Bruno Martelli
- Nathan M. Dunfield
- E. Hironaka
- Curtis T. McMullen
- Jacob Rasmussen
- Akshay Venkatesh
- F. Catanese
In Mathematical Physics
- John William Aaber
- Bruno Martelli
- Nathan M. Dunfield
- E. Hironaka
- Curtis T. McMullen
- Jacob Rasmussen
- Akshay Venkatesh
- F. Catanese
Citations in the corpus
- Closed surface bundles of least volume (2010, methodology): “Like the Whitehead complement, it can be built by gluing the sides of a regular ideal octahedron in H(3) (see [1]); thus its volume is”
- An Introduction to Geometric Topology (2016, methodology): “It is conjectured in [1] that each link in Fig.”