Patterns in odd Khovanov homology

Details Patterns in odd Khovanov homology Patterns in odd Khovanov homology

2011-01-28

arxiv.org/abs/1101.5607v2

Mathematics

Geometric Topology

17 pages, 12 figures; v.2: statements about mutation invariance and transversely non-simple knots are clarified; to appear in

Scientific paper

We investigate properties of the odd Khovanov homology, compare and contrast them with those of the original (even) Khovanov homology, and discuss applications of the odd Khovanov homology to other areas of knot theory and low-dimensional topology. We show that it provides an effective upper bound on the Thurston-Bennequin number of Legendrian links and can be used to detect quasi-alternating knots. A potential application to detecting transversely non-simple knots is also mentioned.

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