A spectral sequence for Khovanov homology with an application to (3<i>,q</i>)–torus links

Turner, Paul

doi:10.2140/agt.2008.8.869

Cited by 33 publications

(41 citation statements)

References 9 publications

(19 reference statements)

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“…The construction of thereof is the main goal of this section. In the non-equivariant case similar spectral sequence was constructed in [Tur08,ET12]. (1) If i ∈ {0, 1, x} define |α| i = #α −1 (i).…”

Section: The Skein Spectral Sequencementioning

confidence: 99%

Equivariant Khovanov Homology of Periodic Links

Politarczyk¹

2019

Michigan Math. J.

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The purpose of this paper is to construct and study equivariant Khovanov homology -a version of Khovanov homology theory for periodic links. Since our construction works regardless of the characteristic of the coefficient ring it generalizes a previous construction by Chbili. We establish invariance under equivariant isotopies of links and study algebraic properties of integral and rational version of the homology theory. Moreover, we construct a skein spectral sequence converging to equivariant Khovanov homology and use this spectral sequence to compute, as an example, equivariant Khovanov homology of torus links T (n, 2).

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Section: The Skein Spectral Sequencementioning

confidence: 99%

Equivariant Khovanov Homology of Periodic Links

Politarczyk¹

2019

Michigan Math. J.

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“…Stošić [30] and Turner [32] independently calculated the rational Khovanov homology of the (3, 3n + i)-torus link, where i = 0, 1, 2.…”

Section: On the Turaev Genus Of A Non-split Linkmentioning

confidence: 99%

The Dealternating Number and the Alternation Number of a Closed 3-Braid

Abe

Kishimoto

2010

J. Knot Theory Ramifications

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“…We give a proof of the lemma again in Appendix A, which is slightly different from Khovanov's. We use the method for calculating Khovanov homology, which was developed in [23] and [27].…”

Section: The Turaev Genus Of An Adequate Knotmentioning

confidence: 99%

The Turaev genus of an adequate knot

Abe¹

2009

Topology and its Applications

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The Turaev genus of a knot is an obstruction to the knot being alternating. An adequate knot is a generalization of an alternating knot. A natural problem is a characterization of the Turaev genus of an adequate knot. In this paper, we show that the Turaev genus of an adequate knot is realized by the genus of the Turaev surface associated to an adequate diagram of the knot using the Khovanov homology. As a result, we obtain the additivity of the Turaev genus of adequate knots, and show that the Turaev genus of an adequate knot is "often" preserved under mutation. We also show that an n-semi-alternating knot is of Turaev genus n. This is the first examples of adequate knots of Turaev genus two or more.

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A spectral sequence for Khovanov homology with an application to (3,q)–torus links

Abstract: We extend the skein exact sequence of Khovanov homology to a spectral sequence which converges to Khovanov homology. We apply this to calculate the rational Khovanov homology of three-stranded torus links.

Cited by 33 publications

References 9 publications

Equivariant Khovanov Homology of Periodic Links

Equivariant Khovanov Homology of Periodic Links

The Dealternating Number and the Alternation Number of a Closed 3-Braid

The Turaev genus of an adequate knot

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