The lens space realization problem
By J. Greene. 2010
104 citations recorded by the source corpus.
We determine the lens spaces that arise by integer Dehn surgery along a knot in the three-sphere. Specically, if surgery along a knot produces a lens space, then there exists an equivalent surgery along a Berge knot with the same knot Floer homology groups. This leads to sharp information about the genus of such a knot. The arguments rely on tools from Floer homology and lattice theory. They are primarily combinatorial in nature.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/758055c42841bfd652e18c824187aa796113a039
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In Computational Theory and Mathematics
- A. Stipsicz
- Peter S. Ozsv'ath
- Zolt'an Szab'o
- M. Hedden
- Jacob Rasmussen
- Yi Ni
- Jennifer Hom
- Ciprian Manolescu
In Geometry and Topology
- A. Stipsicz
- Peter S. Ozsv'ath
- Zolt'an Szab'o
- Ciprian Manolescu
- P. Lisca
- Jacob Rasmussen
- John A. Baldwin
- M. Hedden
In Mathematical Physics
- A. Stipsicz
- Peter S. Ozsv'ath
- Zolt'an Szab'o
- Ciprian Manolescu
- Jacob Rasmussen
- M. Hedden
- John A. Baldwin
- Ian Zemke
Citations in the corpus
- L-space surgeries, genus bounds, and the cabling conjecture (2010, unknown): “4, Proposition 1.3] for p9, which under the same assumptions establishes that 2g(K) 1 p 4 for the specic case of a torus knot K. For the case of a lens space surgery, we establish the bound (3) in [14]. L-SPACE SURGERIES, GENUS BOUNDS, AND THE CABLING CONJECTURE 3 Theorem 1.2. Suppose that KˆS3, pis”
- Grid Homology for Knots and Links (2015, background): “It can also be used to give obstructions on knots admitting lens space surgeries [80, 177, 192]; see also [114].”