Cables of thin knots and bordered Heegaard Floer homology

By Ina Petkova. 2009

89 citations recorded by the source corpus.

We use bordered Floer homology to give a formula for the knot Floer homology of any (p, pn+1)-cable of a thin knot K in terms of Delta_K(t), tau(K), p, and n. We also give a formula for the Ozsvath-Szabo concordance invariant tau(K_{p, pn+1}) in terms of tau(K), p, and n, and a formula for tau(K_{p,q}) for almost all relatively prime p and q.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/4ed5647e04d2c90fb6c6d98de05ee0b88786fe45

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Citations in the corpus

Bordered Heegaard Floer homology and the tau‐invariant of cable knots (2012, methodology): “In [17, Lemma 5], Petkova constructs model complexes for CFK∞(K) of homologically thin knots, and shows that if τ(K) = n, then the model complex contains a direct summand isomorphic to CFK∞(T2,2n+1) if n > 0 and CFK∞(T2,2n−1) if n 0.”
Concordance homomorphisms from knot Floer homology (2014, methodology): “We prefer instead to proceed using bordered Floer homology (see [16, Chapter 11] for n = 2 and [33] for general n; see also [9]), as the computation will serve as a warm-up to a later computation given in Lemma 8.”
Moving basepoints and the induced automorphisms of link Floer homology (2011, background): “5In [16], they do it for bigraded complexes; however, the proof goes through for singly graded complexes like the one under consideration.”
AN INTRODUCTION TO KNOT FLOER HOMOLOGY (2014, unknown): “See [Pet13, OS05a].”
NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE (2014, methodology): “Another strategy for determining absolute Alexander gradings, used by the author in [15] and by Petkova in [24], is first to compute the relative Alexander grading on CFK(Y, P (K)) as described in [16], and then to pin down the absolute grading using the symmetry of knot Floer homology [21, Equation”
Bordered Floer homology for manifolds with torus boundary via immersed curves (2016, background): “cally simplied (in the sense of [21, Section 11]) has a loop-type complement; compare Hom [13]. For example, any thin knot (in particular, any alternating knot) satises this hypothesis; see Petkova [29]. In fact, the authors are unaware of any knot in S3 whose knot Floer homology does not have this ”
On the geography and botany of knot Floer homology (2014, background): “Floer homology is also well-understood under more general satellite operations [26, 27, 28, 36, 47, 76, 78].”