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Surfaces in 4-manifolds behaving badly


Speaker: Kyle Hayden, Columbia University
Location: Zoom
Start time: Tue, Nov 10 2020, 1:10PM

Corks are special contractible 4-manifolds that play a key role in the study of exotic smooth 4-manifolds. In this talk, I will describe applications of corks to the study of surfaces in 4-manifolds. I’ll begin with some badly behaved 2-spheres in 4-space (based on joint work with Piccirillo). Then I’ll use a twist on these ideas to construct smoothly (indeed, holomorphically!) embedded disks in the 4-ball that are isotopic through ambient homeomorphisms but not through diffeomorphisms. There will be lots of cartoons.