Computations of Heegaard-Floer Knot Homology

Baldwin, John A.; Gillam, W. D.

doi:10.1142/s0218216512500757

Cited by 42 publications

(115 citation statements)

References 18 publications

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“…A table with calculations for all non-alternating knots with up to 12 crossings can be found in [BG12].…”

Section: Properties and Applicationsmentioning

confidence: 99%

An introduction to knot Floer homology

Manolescu¹

2016

Physics and Mathematics of Link Homology

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Abstract. This is a survey article about knot Floer homology. We present three constructions of this invariant: the original one using holomorphic disks, a combinatorial description using grid diagrams, and a combinatorial description in terms of the cube of resolutions. We discuss the geometric information carried by knot Floer homology, and the connection to three-and four-dimensional topology via surgery formulas. We also describe some conjectural relations to Khovanov-Rozansky homology.

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“…A table with calculations for all non-alternating knots with up to 12 crossings can be found in [BG12].…”

Section: Properties and Applicationsmentioning

confidence: 99%

An introduction to knot Floer homology

Manolescu¹

2016

Physics and Mathematics of Link Homology

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“…In general, it is difficult to calculate HF K explicitly. However, we might refer to [1,24] for a combinatorial method for the calculation of the above Heegaard Floer homology.…”

Section: The Khovanov Cohomology Of Kanenobu Knotsmentioning

confidence: 99%

A Recursive Formula for the Khovanov Cohomology of Kanenobu Knots

Lei¹,

Zhang²

2017

Bulletin of the Korean Mathematical Society

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Abstract. Kanenobu has given infinite families of knots with the same HOMFLY polynomial invariant but distinct Alexander module structure. In this paper, we give a recursive formula for the Khovanov cohomology of all Kanenobu knots K(p, q), where p and q are integers. The result implies that the rank of the Khovanov cohomology of K(p, q) is an invariant of p + q. Our computation uses only the basic long exact sequence in knot homology and some results on homologically thin knots.

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“…(5) The τ -invariant has been calculated for all knots with up to 11 crossings by Baldwin and Gillam (see [BG06]), it does not detect the unknotting number for any of the above non-alternating knots with up to 11 crossings. (6) Arguably 11n 148 is the most interesting example.…”

Section: 4mentioning

confidence: 99%

The unknotting number and classical invariants, I

Borodzik

Friedl

2015

Algebr. Geom. Topol.

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Abstract. Given a knot K we introduce a new invariant coming from the Blanchfield pairing and we show that it gives a lower bound on the unknotting number of K. This lower bound subsumes the lower bounds given by the Levine-Tristram signatures, by the Nakanishi index and it also subsumes the Lickorish obstruction to the unknotting number being equal to one. Our approach in particular allows us to show for 25 knots with up to 12 crossings that their unknotting number is at least three, most of which are very difficult to treat otherwise.

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Computations of Heegaard-Floer Knot Homology

Cited by 42 publications

References 18 publications

An introduction to knot Floer homology

An introduction to knot Floer homology

A Recursive Formula for the Khovanov Cohomology of Kanenobu Knots

The unknotting number and classical invariants, I

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