Winding homology of knotoids

Deniz Kutluay

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arXiv · 2002.07871

Winding homology of knotoids

Deniz Kutluay

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Abstract

Knotoids were introduced by V. Turaev as open-ended knot-type diagrams that generalize knots. Turaev defined a two-variable polynomial invariant of knotoids which encompasses a generalization of the Jones knot polynomial to knotoids. We define a triply-graded homological invariant of knotoids categorifying the Turaev polynomial, called winding homology. Forgetting one of the three gradings gives a generalization of the Khovanov knot homology to knotoids.

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Deniz Kutluay. 2020-02-18. Winding homology of knotoids. https://arxiv.org/abs/2002.07871

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