Knot Floer homology of Whitehead doubles

By M. Hedden. 2006

125 citations recorded by the source corpus.

In this paper we study the knot Floer homology invariants of the twisted and untwisted Whitehead doubles of an arbitrary knot, K . A formula is presented for the filtered chain homotopy type of b HFK.D .K;t// in terms of the invariants for K , where D .K;t/ denotes the t ‐twisted positive (resp. negative)-clasped Whitehead double of K . In particular, the formula can be used iteratively and can be used to compute the Floer homology of manifolds obtained by surgery on Whitehead doubles. An immediate corollary is that . DC.K;t//D1 if t 0 are not smoothly slice. Another corollary is a closed formula for the Floer homology of the three-manifold obtained by gluing the complement of an arbitrary knot, K , to the complement of the trefoil.

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

View Paper: https://www.semanticscholar.org/paper/cfc66a06a89dbf2ee742df25732784c9315a6014

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The decategorification of sutured Floer homology (2009, methodology): “The group ĤFK(K(n)) has been studied by Eftekhary [5] (in the case n = 0) and Hedden [10], who gives a complete calculation in terms of the groups HFK−(K); see also [20, Section 10].”
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].”
Topologically slice knots of smooth concordance order two (2012, background): “The key idea from [13] was to observe that with the addition of anot er basepoint, the natural Heegaard diagram for −N–framed surgery on K could be made to represent the knot μ ⊂ Y−N (K).”
On Floer homology and the Berge conjecture on knots admitting lens space surgeries (2007, methodology): “Thus our proof of Theorem 1.4 will focuses on parts (2) and (3). We begin by recalling Theorem 1.2 of [ 12 ].”
Bordered Heegaard Floer homology and the tau‐invariant of cable knots (2012, background): “Studying τ has yielded many nice results, such as a new proof of the Milnor conjecture [12], and examples of Alexander polynomial one knots which are not smoothly slice (for example, [4, 10]).”
Concordance homomorphisms from knot Floer homology (2014, methodology): “(Hedden, [7]) For the 0-twisted Whitehead double of the right-handed trefoil (with its positive clasp), the knot Floer homology has 15 generators, which we denote ir, jr, kr for r = 0, 1, 2, 3 and ls for s = 1, 2, 3.”