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Knotted 3-balls in the 4-sphere


Speaker: David Gabai, Princeton University
Location: Zoom
Start time: Tue, Apr 13 2021, 1:10PM

We give examples of codimension-1 knotting in the 4-sphere, i.e. there are 3-balls $B_1$ with boundary the standard 2-sphere, which are not isotopic rel boundary to the standard 3-ball $B_0$. In fact isotopy classes of such balls form a group which is infinitely generated. The existence of knotted balls implies that there exists inequivalent fiberings of the unknot in the 4-sphere, in contrast to the situation in dimension-3. Also, that there exists diffeomorphisms of $S^1\times B^3$ homotopic rel boundary to the identity, but not isotopic rel boundary to the identity. Joint work with Ryan Budney.