Fibered ribbon disks

Larson, Kyle and Meier, J. (2015) Fibered ribbon disks. JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS, 24 (14). ISSN 0218-2165

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Abstract

We study the relationship between fibered ribbon 1–knots and fibered ribbon 2–knots by studying fibered slice disks with handlebody fibers. We give a characterization of fibered homotopy-ribbon disks and give analogues of the Stallings twist for fibered disks and 2–knots. As an application, we produce infinite families of distinct homotopy-ribbon disks with homotopy equivalent exteriors, with potential relevance to the Slice-Ribbon Conjecture. We show that any fibered ribbon 2– knot can be obtained by doubling infinitely many different slice disks (sometimes in different contractible 4–manifolds). Finally, we illustrate these ideas for the examples arising from spinning fibered 1–knots.

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