## Nonsimple, ribbon fibered knots

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- by Katura Miyazaki
- Trans. Amer. Math. Soc.
**341**(1994), 1-44 - DOI: https://doi.org/10.1090/S0002-9947-1994-1176509-4
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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 $(p,q)$ cable of a fibered knot $k$ is ribbon where $p(> 1)$ is the winding number of a cable in ${S^1} \times {D^2}$, then $q = \pm 1$ and $k$ is ribbon.

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## Bibliographic Information

- © Copyright 1994 American Mathematical Society
- 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