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Extremal Khovanov homology of Turaev genus one links

Volume 250 / 2020

Oliver T. Dasbach, Adam M. Lowrance Fundamenta Mathematicae 250 (2020), 63-99 MSC: Primary 57M27; Secondary 57M25. DOI: 10.4064/fm729-9-2019 Published online: 17 January 2020

Abstract

The Turaev genus of a link can be thought of as a way of measuring how nonalternating a link is. A link is Turaev genus zero if and only if it is alternating, and in this viewpoint, links with large Turaev genus are very nonalternating. In this paper, we study Turaev genus one links, a class of links which includes almost alternating links. We prove that the Khovanov homology of a Turaev genus one link is isomorphic to $\mathbb {Z}$ in at least one of its extremal quantum gradings. As an application, we compute or nearly compute the maximal Thurston Bennequin number of a Turaev genus one link.

Authors

  • Oliver T. DasbachDepartment of Mathematics
    Louisiana State University
    Baton Rouge, LA 70803, U.S.A.
    e-mail
  • Adam M. LowranceDepartment of Mathematics
    Vassar College
    Poughkeepsie, NY 12604-0257, U.S.A.
    e-mail

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