The Classification of Spun Torus Knots
Blake Winter

TL;DR
This paper investigates the properties of a construction linking welded knots to ribbon torus knots, revealing its non-injective nature and providing an algebraic classification for classical knots.
Contribution
It demonstrates the non-injectivity of Satoh's construction and offers an algebraic classification when restricted to classical knots.
Findings
The construction is surjective but not injective.
Peripheral structure invariant restricts the failure of injectivity.
Classifies the construction algebraically for classical knots.
Abstract
S. Satoh has defined a construction to obtain a ribbon torus knot given a welded knot. This construction is known to be surjective. We show that it is not injective. Using the invariant of the peripheral structure, it is possible to provide a restriction on this failure of injectivity. In particular we also provide an algebraic classification of the construction when restricted to classical knots, where it is equivalent to the torus spinning construction.
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 · Orthopedic Surgery and Rehabilitation · Congenital limb and hand anomalies
