Members’ Seminar

We give the first examples of codimension-1 knotting in the 4-sphere, i.e. there is a 3-ball B1 with boundary the standard linear 2-sphere, which is not isotopic rel boundary to the standard linear 3-ball B0. 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 S1 x B3 homotopic rel boundary to the identity, but not isotopic rel boundary to the identity. Joint work with Ryan Budney