Lens space surgeries and L-space homology spheres

By Jacob Rasmussen. 2007

87 citations recorded by the source corpus.

We describe necessary and sufficient conditions for a knot in an L-space to have an L-space homology sphere surgery. We use these conditions to reformulate a conjecture of Berge about which knots in S^3 admit lens space surgeries.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f3997c5305c0babb7deed4f000b9d5d2ff51f22b

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Floer simple manifolds and L-space intervals (2015, unknown): “For the most part, these are straightforward extensions of results in [39],[44], and [4].”
On Knot Floer Homology and Cabling: 2 (2008, unknown): “Suppose that Kp,pn+1 is a C-knot.”
The lens space realization problem (2010, background): “Rasmussen [32], who have proposed programs to settle Conjecture 1.”
L-space surgeries, genus bounds, and the cabling conjecture (2010, methodology): “Rasmussen established the inequality p− 5 2 ≤ 2g(K)− 1 Partially supported by an NSF Post-doctoral Fellowship.”
The decategorification of sutured Floer homology (2009, background): “urgery on K), and let K(n) ⊂Kn be the core circle of the ﬁlling. Then SFH(S3(R)) is isomorphic to HFK\(K(n)). Its Euler characteristic is given by τ(S3(R)) ∼∆ K(t)· tn −1 t−1 , cf. Proposition 3.1 of [Ra07]. Note that when n= 0, the torsion vanishes, regardless of what Kis. The group HFK\(K(n)) has ”
On Floer homology and the Berge conjecture on knots admitting lens space surgeries (2007, methodology): “I also thank Cameron Gordon for generous sharing of his knowledge of Dehn surgery, and Jake Rasmussen for sharing his independent work on Floer homology and the Berge conjecture.”