Bordered Heegaard Floer homology and the tau‐invariant of cable knots

By Jennifer Hom. 2012

113 citations recorded by the source corpus.

We define a concordance invariant, ε(K), associated to the knot Floer complex of K, and give a formula for the Ozsváth–Szabó concordance invariant τ of Kp,q, the (p, q)‐cable of a knot K, in terms of p, q, τ(K), and ε(K). We also describe the behavior of ε under cabling, allowing one to compute τ of iterated cables. Various properties and applications of ε are also discussed.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/3a828c2e66bc83aba4a7d8d4fa1dac7cb5cfd8c0

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In Discrete Mathematics and Combinatorics

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Citations in the corpus

AN INTRODUCTION TO KNOT FLOER HOMOLOGY (2014, unknown): “By using the full knot Floer complex, one can extract additional concordance invariants; see [Hom14b, Hom15, HW14].”
An infinite-rank summand of topologically slice knots (2013, unknown): “K/; see the author [19].”
Bordered Floer homology for manifolds with torus boundary via immersed curves (2016, background): “in a neighborhood of a meridian passing through the peg except for one segment which has slope 2˝(K) (K), where ˝(K) is the Ozsvath-Szabo concordance invaraiant and is the invariant dened by Hom [13]. In the other direction, it is also shown in [21] that HFK [can be recovered from CFD; we can ask if”
A survey on Heegaard Floer homology and concordance (2015, methodology): “…Heegaard Floer theory: • Ozsváth-Szabó’s Z-valued invariant τ [OS03b], • Ozsváth-Szabó’s Z-valued invariant ν [OS11], • the author’s {−1, 0, 1}-valued invariant ε [Hom14b], • the author and Wu’s ν+ (equivalently, ν−) invariant [HW16], based on work of Rasmussen [Ras03], • the sequence of…”
NONSURJECTIVE SATELLITE OPERATORS AND PIECEWISE-LINEAR CONCORDANCE (2014, methodology): “Hom [9] found a formula for τ(Jp,q) in terms of τ(J) and ǫ(J).”
Concordance homomorphisms from knot Floer homology (2014, methodology): “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 [36] for general n; see also [14]), as the computation will serve as a warm-up to a later computation given in Lemma 8.8, where T”
On the geography and botany of knot Floer homology (2014, background): “In [33], Hom defined a {−1, 0, 1}-valued invariant of an infinity complex, C .”