Transverse knots and Khovanov homology

Olga Plamenevskaya

doi:10.4310/MRL.2006.v13.n4.a7

Transverse knots and Khovanov homology

Olga Plamenevskaya

Mathematics

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66 Scopus citations

Abstract

We define an invariant of transverse links in (S³, ξ_std) as a distinguished element of the Khovanov homology of the link. The quantum grading of this invariant is the self-linking number of the link. For knots, this gives a bound on the self-linking number in terms of Rasmussen's invariant s(K). We prove that our invariant vanishes for transverse knot stabilizations, and that it is non-zero for quasipositive braids. We also discuss a connection to Heegaard Floer invariants.

Original language	English
Pages (from-to)	571-586
Number of pages	16
Journal	Mathematical Research Letters
Volume	13
Issue number	4
DOIs	https://doi.org/10.4310/MRL.2006.v13.n4.a7
State	Published - Jul 2006

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title = "Transverse knots and Khovanov homology",

abstract = "We define an invariant of transverse links in (S3, ξstd) as a distinguished element of the Khovanov homology of the link. The quantum grading of this invariant is the self-linking number of the link. For knots, this gives a bound on the self-linking number in terms of Rasmussen's invariant s(K). We prove that our invariant vanishes for transverse knot stabilizations, and that it is non-zero for quasipositive braids. We also discuss a connection to Heegaard Floer invariants.",

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AB - We define an invariant of transverse links in (S3, ξstd) as a distinguished element of the Khovanov homology of the link. The quantum grading of this invariant is the self-linking number of the link. For knots, this gives a bound on the self-linking number in terms of Rasmussen's invariant s(K). We prove that our invariant vanishes for transverse knot stabilizations, and that it is non-zero for quasipositive braids. We also discuss a connection to Heegaard Floer invariants.

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DO - 10.4310/MRL.2006.v13.n4.a7

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AN - SCOPUS:33748931620

SN - 1073-2780

VL - 13

SP - 571

EP - 586

JO - Mathematical Research Letters

JF - Mathematical Research Letters

IS - 4

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Transverse knots and Khovanov homology

Abstract

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