Fibered ribbon disks

Kyle Larson; Jeffrey Meier

doi:10.1142/s0218216515500662

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arXiv · 1410.4854

Fibered ribbon disks

Kyle Larson·Jeffrey Meier

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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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Kyle Larson, Jeffrey Meier. 2014-10-17. Fibered ribbon disks. https://doi.org/10.1142/s0218216515500662

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