Near extremal Khovanov homology of Turaev genus one links. (English) Zbl 1539.57010
It is well-known that a link is alternating if and only if its Turaev genus is zero and so we can view Tureav genus one links as being close to alternating links. Therefore, we expect that this class of links shares some common properties with the class of alternating links. In this paper, the authors study the Khovanov homology of a Turaev genus one link in the first and last two polynomial gradings where the homology is nontrivial. They show that a particular summand in the Khovanov homology of a Turaev genus one link is trivial. This trivial summand leads to a computation of the Rasmussen \(s\)-invariant and to bounds on the smooth four genus for certain Turaev genus one knots.
Reviewer: Khaled Qazaqzeh (Irbid)
MSC:
| 57K18 | Homology theories in knot theory (Khovanov, Heegaard-Floer, etc.) |
References:
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