Winding homology of knotoids
Geometric Topology
2020-09-29 v2
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.
Keywords
Cite
@article{arxiv.2002.07871,
title = {Winding homology of knotoids},
author = {Deniz Kutluay},
journal= {arXiv preprint arXiv:2002.07871},
year = {2020}
}
Comments
33 pages, 28 figures; added Remarks 4.7, 4.8, 6.3; minor changes in notation; clarifications added; typos fixed; references added