The paper proves a Kirby-Siebenmann obstruction criterion for smoothing topological pseudo-isotopies of 4-manifolds, gives new positive cases for certain fundamental groups, and constructs the first diffeomorphisms that are topologically but not smoothly pseudo-isotopic to the identity.
Light bulb smoothing for topological surfaces in 4-manifolds
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abstract
We present new smoothing techniques for topologically embedded surfaces in smooth 4-manifolds, which give topological isotopy to a smooth surface. As applications, we prove "topological = smooth" results in dimension 4 for certain disks and spheres modulo isotopy. A key step in our approach is to link Quinn's smoothing theory with ideas in Gabai's 4-dimensional light bulb theorem and succeeding developments of Schneiderman-Teichner and Kosanovi\'c-Teichner. As another application of our smoothing technique, we obtain a topological version of the Dax invariant which gives topological isotopy obstructions for topological disks in 4-manifolds.
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Smoothing topological pseudo-isotopies of 4-manifolds
The paper proves a Kirby-Siebenmann obstruction criterion for smoothing topological pseudo-isotopies of 4-manifolds, gives new positive cases for certain fundamental groups, and constructs the first diffeomorphisms that are topologically but not smoothly pseudo-isotopic to the identity.