Document Type

Article

Publication Date

7-6-2020

Keywords

4-manifold, Link concordance, milnor invariants, shake slice

Abstract

© 2020 World Scientific Publishing Company. We can construct a 4-manifold by attaching 2-handles to a 4-ball with framing r along the components of a link in the boundary of the 4-ball. We define a link as r-shake slice if there exists embedded spheres that represent the generators of the second homology of the 4-manifold. This naturally extends r-shake slice, a generalization of slice that has previously only been studied for knots, to links of more than one component. We also define a relative notion of shaker-concordance for links and versions with stricter conditions on the embedded spheres that we call stronglyr-shake slice and stronglyr-shake concordance. We provide infinite families of links that distinguish concordance, shake concordance, and strong shake concordance. Moreover, for r = 0 we completely characterize shake slice and shake concordant links in terms of concordance and string link infection. This characterization allows us to prove that the first non-vanishing Milnor μ¯ invariants are invariants of shake concordance. We also argue that shake concordance does not imply link homotopy.

Journal Title

Journal of Knot Theory and its Ramifications

Volume

29

Issue

12

First Page

2050087

DOI

https://doi.org/10.1142/S021821652050087X

First Department

Mathematics

Acknowledgements

Retrieved January 11, 2021 from https://arxiv.org/pdf/1902.06807.pdf

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