Lens space surgeries and a conjecture of Goda and Teragaito

By Jacob Rasmussen. 2004

87 citations recorded by the source corpus.

Using work of Ozsvath and Szabo, we show that if a nontrivial knot in S 3 admits a lens space surgery with slope p, then p � 4g+3, where g is the genus of the knot. This is a close approximation to a bound conjectured by Goda and Teragaito.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/1c906655a29868d280d3a3cf73d1341eb647d852

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

On Floer homology and the Berge conjecture on knots admitting lens space surgeries (2007, background): “On which knots in the three-sphere can one perform Dehn surgery and obtain a lens space? This question has received considerable attention in recent years [4, 5, 19, 24, 10, 30, 1, 2] and much progress has been made towards a general method of enumeration of such knots.”
On Knot Floer Homology and Cabling: 2 (2008, background): “One area of low-dimensional topology where the Ozsváth-Szabó invariants have had a significant impact is in the study of Dehn surgery [1, 5, 7, 20, 28, 23, 22, 34, 32, 39].”
Involutive Heegaard Floer homology (2015, methodology): “Different conventions are used in [49]; with h0 as defined there, we have V0(K) = h0(K ∗), where K∗ is the mirror of K.”
On the geography and botany of knot Floer homology (2014, background): “This is essentially an invariant defined byRasmussen [79,80] in analogy to an invariant of Frøyshov from instanton homology [18].”
On knot Floer homology and cabling (2004, background): “ [13, 37]. 1.1.3. Cable knots and lens space (L-space) surgeries. One area of low-dimensional topology where the Ozsvath-Szab´o invariants have had a signiﬁcant impact is in the study of Dehn surgery [1, 5, 7, 20, 28, 23, 22, 34, 32, 39]. Many of these results draw on the close relationship between ”
Grid Homology for Knots and Links (2015, background): “The invariants hk are the “local h-invariants” considered by Rasmussen in [191, 192] (compare also [61]).”
Concordance homomorphisms from knot Floer homology (2014, background): “The bounds on the slice genus are no stronger than the bounds coming from Rasmussen’s “local h invariants” [34]; see also [15, 35].”