Knot Floer homology of (1,1)-knots
Hiroshi Goda, Hiroshi Matsuda, Takayuki Morifuji
TL;DR
This paper introduces a combinatorial approach to compute knot Floer homology for (1,1)-knots, enabling the determination of unknotting numbers and 4-genera for specific complex knots.
Contribution
It develops a new combinatorial method for calculating knot Floer homology of (1,1)-knots and applies it to complex examples.
Findings
Calculated knot Floer homology for non-alternating (1,1)-knots with ten crossings.
Determined unknotting numbers of certain pretzel knots.
Established 4-genera for specific pretzel knots.
Abstract
We present a combinatorial method for a calculation of knot Floer homology with Z-coefficient of (1,1)-knots, and then demonstrate it for non-alternating (1,1)-knots with ten crossings and the pretzel knots of type (-2,m,n). Our calculations determine the unknotting numbers and 4-genera of the pretzel knots of this type.
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 · Homotopy and Cohomology in Algebraic Topology · Botulinum Toxin and Related Neurological Disorders