The Khovanov-Rozansky Cohomology and Bennequin Inequalities
Hao Wu
TL;DR
This paper reviews and extends Bennequin inequalities using Khovanov-Rozansky cohomology, providing new proofs and inequalities that generalize previous results with Gornik's version.
Contribution
It offers a new proof of a Bennequin inequality and introduces new inequalities for knots based on Gornik's Khovanov-Rozansky cohomology, expanding prior work.
Findings
New proof of a Bennequin type inequality.
Derived new inequalities for knots using Gornik's cohomology.
Generalized previous inequalities by Shumakovitch, Plamenevskaya, and Kawamura.
Abstract
We review Bennequin type inequalities established using various versions of the Khovanov-Rozansky cohomology. Then we give a new proof of a Bennequin type inequality established by the author, and derive new Bennequin type inequalities for knots using Gornik's version of the Khovanov-Rozansky cohomology, which generalize those established by Shumakovitch, Plamenevskaya and Kawamura using the Rasmussen invariant.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Combinatorial Mathematics · Organometallic Compounds Synthesis and Characterization