Minimum volume cusped hyperbolic three-manifolds
By David Gabai, R. Meyerhoff, Peter Milley. 2007
134 citations recorded by the source corpus.
This paper is the second in a series whose goal is to understand the structure of low-volume complete orientable hyperbolic 3-manifolds. Using Mom technology, we prove that any one-cusped hyperbolic 3-manifold with volume <= 2.848 can be obtained by a Dehn filling on one of 21 cusped hyperbolic 3-manifolds. We also show how this result can be used to construct a complete list of all one-cusped hyperbolic three-manifolds with volume <= 2.848 and all closed hyperbolic three-manifolds with volume <= 0.943. In particular, the Weeks manifold is the unique smallest volume closed orientable hyperbolic 3-manifold.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f0526a8c84c5d3ca1f5557560dcaf636e4623265
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Applied Mathematics
- .Ilker S. Yuce
- D. Rolfsen
- Adam Clay
- Akshay Venkatesh
- Ian Agol
- Marc Lackenby
- R. Meyerhoff
- Michael Kapovich
In Geometry and Topology
- Akshay Venkatesh
- .Ilker S. Yuce
- Ian Agol
- Adam Clay
- D. Rolfsen
- Marc Lackenby
- Frank Calegari
- R. Meyerhoff
In Mathematical Physics
- Akshay Venkatesh
- .Ilker S. Yuce
- Adam Clay
- Ian Agol
- D. Rolfsen
- Marc Lackenby
- Frank Calegari
- R. Meyerhoff
Citations in the corpus
- The maximal number of exceptional Dehn surgeries (2008, background): “MARC LACKENBY AND ROBERT MEYERHOFF”
- Two-generator free Kleinian groups and hyperbolic displacements (2009, result): “Although the bounds given in [8] and [3] are superseded by the recent works of Gabai– Meyerhoff–Milley [ 11], [12] and Milley [17] using a newer approach, Mom technology, it is conceivable that an improvement in the lower bound for the displacements under the isometries described in the log 3 theore”
- The minimal volume orientable hyperbolic 2-cusped 3-manifolds (2008, background): “Recently, Gabai, Meyerhoff and Milley have identified the smallest volume orientable hyperbolic 3-manifold to be the Fomenko-Matveev-Weeks manifold, with volume 0.9427 . . . [11].”
- A torsion Jacquet--Langlands correspondence (2012, background): “The Weeks manifold is the smallest volume arithmetic manifold [23], as well as the smallest volume orientable hyperbolic manifold [39].”
- Ordered Groups and Topology (2015, methodology): “The Weeks manifold W described by surgery as in Figure 2 is the closed hyperbolic 3-manifold of least volume [34].”