Traces of links and simply connected 4-manifolds

Cavallo, Alberto and Stipsicz, András (2023) Traces of links and simply connected 4-manifolds. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 55 (1). pp. 321-337. ISSN 0024-6093

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Abstract

We study the set SˆM of framed smoothly slice links which lie on the boundary of the complement of a 1-handlebody in a closed, simply connected, smooth 4-manifold M. We show that SˆM is well-defined and describe how it relates to exotic phenomena in dimension four. In particular, in the case when X is smooth, with a handle decompositions with no 1-handles and homeomorphic to but not smoothly embeddable in D4, our results tell us that X is exotic if and only if there is a link L↪S3 which is smoothly slice in X, but not in D4. Furthermore, we extend the notion of high genus 2-handle attachment, introduced by Hayden and Piccirillo, to prove that exotic 4-disks that are smoothly embeddable in D4, and therefore possible counterexamples to the smooth 4-dimensional Schönflies conjecture, cannot be distinguished from D4 only by comparing the slice genus functions of links.

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