On transverse invariants from Khovanov-type homologies
Carlo Collari
备注：
29 pages, 10 figures. Major revisions. Introduction rewritten, added a result on the vanishing of the Plamenevskaya invariant, uniqueness property generalised, added a section explaining how to use the invariants to distinguish transverse link, and some changes in the structure
发表信息：
J. Knot Theory Ramifications 28 (2019), no. 1, 1950012, 37 pp
In this article we introduce a family of transverse invariants arising from the deformations of Khovanov homology. This family includes the invariants introduced by Plamenevskaya and by Lipshitz, Ng, and Sarkar. Then, we investigate the invariants arising from Bar-Natan's deformation. These invariants, called $β$-invariants, are essentially equivalent to Lipshitz, Ng, and Sarkar's invariants $ψ^\pm$. From the $β$-invariants we extract two non-negative integers which are transverse invariants (the $c$-invariants). Finally, we give several conditions which imply the non-effectiveness of the $c$-invariants, and use them to prove several vanishing criteria for the Plamenevskaya invariant $[ψ]$, and the non-effectiveness of the vanishing of $[ψ]$, for all prime knots with less than 12 crossings.
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