Fibered ribbon disks
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.
Keywords
Cite
@article{arxiv.1410.4854,
title = {Fibered ribbon disks},
author = {Kyle Larson and Jeffrey Meier},
journal= {arXiv preprint arXiv:1410.4854},
year = {2017}
}
Comments
20 pages, 3 figures. Version two has improved exposition and incorporates referee suggestions. This version has been accepted for publication