Alexander polynomials and signatures of some high-dimensional knots
Eva Bayer-Fluckiger
TL;DR
This paper establishes criteria linking the signature of certain high-dimensional knots to their Alexander polynomial, providing a complete characterization for specific knot types in higher-dimensional spheres.
Contribution
It offers necessary and sufficient conditions connecting knot signatures with square-free Alexander polynomials in high-dimensional knot theory.
Findings
Characterization of signatures for (4q-1)-knots in (4q+1)-spheres
Conditions for Alexander polynomials to correspond to specific signatures
Complete criteria for high-dimensional knot signatures
Abstract
We give necessary and sufficient conditions for an integer to be the signature of a (4q-1)-knot in the (4q+1)-sphere with a given square-free Alexander polynomial.
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 · Algebraic Geometry and Number Theory