The Classification of Spun Torus Knots

Details The Classification of Spun Torus Knots The Classification of Spun Torus Knots

2007-11-11

arxiv.org/abs/0711.1638v3

Mathematics

Geometric Topology

12 pages, 6 figures

Scientific paper

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.

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