Winding homology of knotoids

Deniz Kutluay

备注：: 33 pages, 28 figures; added Remarks 4.7, 4.8, 6.3; minor changes in notation; clarifications added; typos fixed; references added

英文摘要：

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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