Seminar

In 2019, Budney and Gabai introduced barbell diffeomorphisms of 4-manifolds and used them to construct infinitely many “knotted 3-balls” in S^4, i.e. infinitely many 3-balls in S^4 with the same boundary which are pairwise non-isotopic rel. boundary. In joint work with Seungwon Kim and Gheehyun Nahm, we use barbells to construct infinitely many n-component Brunnian links of 3-balls in S^4, i.e. infinitely many n-component collections of 3-balls in S^4 with the same boundary which are (1) pairwise non-isotopic rel. boundary, and (2) become isotopic rel. boundary if any one of the 3-balls in the collection is ignored. In the talk we will go through the definition of barbells and the construction of these Brunnian 3-balls. There will be lots of pictures.