Stable isotopy in four dimensions

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.

24 pages; many color figures; Updated version: 25 pages; minor expository changes; to appear in Journal London Mathematical Society

References in corpus (8)

• Corks, Plugs and exotic structures
• Positive scalar curvature, diffeomorphisms and the Seiberg-Witten invariants
• Variations on Fintushel-Stern Knot Surgery on 4-manifolds
• Round handles, logarithmic transforms, and smooth 4-manifolds
• An obstruction to smooth isotopy in dimension 4
• Topological triviality of smoothly knotted surfaces in 4-manifolds
• Knotting corks
• Isotoping 2-spheres in 4-manifolds

Cited by in corpus (14)

• Corks, exotic 4-manifolds and knot concordance
• On the Frøyshov invariant and monopole Lefschetz number
• Stably slice disks of links
• Isotopy of the Dehn twist on K3#K3 after a single stabilization
• Knotted surfaces in 4-manifolds and stabilizations
• Equivalent non-isotopic spheres in 4-manifolds
• Exotically knotted disks and complex curves
• Positive scalar curvature and higher-dimensional families of Seiberg-Witten equations
• Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group
• An adjunction inequality obstruction to isotopy of embedded surfaces in 4-manifolds
• Nonexistence of twists and surgeries generating exotic 4-manifolds
• A recipe for exotic 2-links in closed 4-manifolds whose components are topological unknots
• Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds
• Infinite nonabelian corks