Nonsimple, ribbon fibered knots

Author:
Katura Miyazaki

Journal:
Trans. Amer. Math. Soc. **341** (1994), 1-44

MSC:
Primary 57M25

DOI:
https://doi.org/10.1090/S0002-9947-1994-1176509-4

MathSciNet review:
1176509

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Abstract: The connected sum of an arbitrary knot and its mirror image is a ribbon knot, however the converse is not necessarily true for all ribbon knots. We prove that the converse holds for any ribbon fibered knot which is a connected sum of iterated torus knots, knots with irreducible Alexander polynomials, or cables of such knots. This gives a practical method to detect nonribbon fibered knots. The proof uses a characterization of homotopically ribbon, fibered knots by their monodromies due to Casson and Gordon. We also study when cable fibered knots are ribbon and results which support the following conjecture.

**Conjecture**. If a cable of a fibered knot is ribbon where is the winding number of a cable in , then and is ribbon.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1994-1176509-4

Keywords:
Ribbon,
homotopically ribbon,
fibered knot,
monodromy,
Johannson's characteristic submanifold

Article copyright:
© Copyright 1994
American Mathematical Society