Stable isotopy in four dimensions

Dave Auckly; Hee Jung Kim; Paul Melvin; Daniel Ruberman

doi:10.1112/jlms/jdu075

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arXiv · 1406.4937

Stable isotopy in four dimensions

Dave Auckly·Hee Jung Kim·Paul Melvin·Daniel Ruberman

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Abstract

We construct infinite families of topologically isotopic but smoothly distinct knotted spheres in many simply connected 4-manifolds that become smoothly isotopic after stabilizing by connected summing with $S^2 \times S^2$, and as a consequence, analogous families of diffeomorphisms and metrics of positive scalar curvature for such 4-manifolds. We also construct families of smoothly distinct links, all of whose corresponding proper sublinks are smoothly isotopic, that become smoothly isotopic after stabilizing.

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Dave Auckly, Hee Jung Kim, Paul Melvin, Daniel Ruberman. 2014-11-11. Stable isotopy in four dimensions. https://doi.org/10.1112/jlms%2Fjdu075

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