A note on cabling and $L$–space surgeries

By Jennifer Hom. 2009

53 citations recorded by the source corpus.

We prove that the (p,q)-cable of a knot K in S^3 admits a positive L-space surgery if and only if K admits a positive L-space surgery and q/p \geq 2g(K)-1, where g(K) is the Seifert genus of K. The "if" direction is due to Hedden.

Subfields: Genetics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f5a7fbb1fd95c0f6c4ba05587d1ab2ac11ecd4c1

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Citations in the corpus

On the geography and botany of knot Floer homology (2014, background): “We could similarly obtain infinite families of prime knots concordant to J by appealing to the known behavior of knot Floer homology under more general satellite operations [26, 27, 28, 36, 78].”
Concordance homomorphisms from knot Floer homology (2014, background): “y, which can be done by a number of diﬀerent techniques; see for example [8]. In fact, according to [10, Theorem 1.10], Cn,2n−1(T 2,3) has an L-space surgery, so one could apply Theorem 6.2; see also [13]. We prefer instead to proceed using bordered Floer homology (see [18, Chapter 11] for n = 2 and”
The knot Floer complex and the smooth concordance group (2011, methodology): “The fact that T2,3; p,p+1 is an L-space knot follows from [Hed09, Theorem 1.10] (cf. [Hom11b]), where Hedden gives sufficient conditions for the cable of an L-space knot to again be an L-space knot.”
More concordance homomorphisms from knot Floer homology (2019, background): “here T 2,3;n,n+1 denotes the (n,n + 1)-cable of T 2,3, instead of the locally equivalent CFKR(Dn,n+1). The advantage of this approach is that T 2,3;n,n+1 is an L-space knot [Hed09, Theorem 1.10] (cf. [Hom11]), and so CFKR(T 2,3;n,n+1) is a standard complex and completely determined by its Alexander ”
Floer simple manifolds and L-space intervals (2015, unknown): “Examples include: • Knots in the solid torus with solid torus surgeries (aka Berge-Gabai knots) • The twisted torus knots T (p, kp± 1; 2, 1) studied by Vafaee [47] • Cables of L-space braids [21] • Satellites where the pattern knot is a Berge-Gabai knot and the companion is an L-space braid [22]”
An infinite-rank summand of topologically slice knots (2013, methodology): “Furthermore, the group CFK is totally ordered [Hom11a, Proposition 4.1], with the ordering given by C1 > C2 if and only if ε(C1 ⊗ C ∗ 2 ) = 1.”