Fibered ribbon disks

TL;DR

This paper explores the relationship between fibered ribbon 1-knots and 2-knots, providing new characterizations, analogues of Stallings twists, and constructing infinite families of homotopy-ribbon disks with potential implications for the Slice-Ribbon Conjecture.

Contribution

It introduces a characterization of fibered homotopy-ribbon disks, develops analogues of Stallings twists for fibered disks and 2-knots, and constructs infinite families of such disks with identical exteriors.

Findings

Characterization of fibered homotopy-ribbon disks

Analogues of Stallings twist for fibered disks and 2-knots

Infinite families of homotopy-ribbon disks with homotopy equivalent exteriors

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.