Knotted 3-balls in the 4-sphere

Abstract: 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 x B^3 homotopic rel boundary to the identity, but not isotopic rel boundary to the identity. (Joint work with Ryan Budney)

Mathematics

Audience: researchers in the topic

MIT Geometry and Topology Seminar

Series comments: Password is "topology".