Knotted 3-balls in the 4-sphere


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February 28, 2020 3:30 pm - 4:30 pm
Science Center 507
Address: 1 Oxford Street, Cambridge, MA 02138 USA

David Gabai - Princeton University

We give the first examples of codimension-1 knotting in the 4-sphere, i.e. there is a 3-ball B_1 with boundary the standard linear 2-sphere, which is not isotopic rel boundary to the standard linear 3-ball B_0. Actually, there is an infinite family of distinct isotopy classes of such balls. This implies that there exist inequivalent fiberings of the unknot in 4-sphere, in contrast to the situation in dimension-3. Also, that there exists diffeomorphisms of S^1 x B^3 homotopic rel boundary to the identity, but not isotopic rel boundary to the identity. Joint work with Ryan Budney.

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