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Узлы и теория представлений
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The Jones polynomial, Khovanov homology, and Turaev genus Adam Lowrance |
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Аннотация: The Turaev surface of a link diagram is a surface built from a cobordism between the all-A and all-B Kauffman states of the diagram, and the Turaev genus of a link is the minimum genus of the Turaev surface for any diagram of the link. The Turaev surface was first used to give simple versions of the Kauffman-Mursaugi-Thistlethwaite proofs of some Tait conjectures. In this talk, we first give a brief history of the Turaev surface, the Turaev genus of a link, and some related applications. We then discuss some recent results on the extremal and near extremal terms in the Jones polynomial and Khovanov homology of a Turaev genus one link. Язык доклада: английский |