TL;DR
This paper resolves the remaining unknown cases of the concordance genus for prime knots with 10 or fewer crossings, using algebraic invariants and twisted Alexander polynomials.
Contribution
It completes the classification of the concordance genus for small prime knots by applying advanced invariants.
Findings
Two cases settled using Levine's algebraic concordance invariants
One case resolved with twisted Alexander polynomials as Casson-Gordon invariants
Provides a complete understanding of concordance genus for prime knots ≤10 crossings
Abstract
The concordance genus of a knot K is the minimum three-genus among all knots concordant to K. For prime knots of 10 or fewer crossings there have been three knots for which the concordance genus was unknown. Those three cases are now resolved. Two of the cases are settled using invariants of Levine's algebraic concordance group. The last case depends on the use of twisted Alexander polynomials, viewed as Casson-Gordon invariants.
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.