Invertible knot concordances and prime knots

Details Invertible knot concordances and prime knots Invertible knot concordances and prime knots

2000-03-05

arxiv.org/abs/math/0003034v1

Mathematics

Geometric Topology

6 pages, 3 figures, LaTeX 2e

Scientific paper

Kirby and Lickorish showed that every knot in the 3-sphere is concordant to a
prime knot, equivalently, every concordance class contains a prime knot. We
prove here that their result can be strengthened: Every knot in the 3-sphere is
invertibly concordant to a prime knot. A consequence is that every double
concordance class contains a prime knot.

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