Knotted handlebodies in the 4-sphere and 5-ball

초록

For every integer g ≥ 2 we construct 3-dimensional genus-g 1-handlebodies smoothly embedded in S4 with the same boundary, and which are defined by the same cut systems of their boundary, yet which are not isotopic rel. boundary via any locally flat isotopy even when their interiors are pushed into B5. This proves a conjecture of Budney–Gabai for genus at least 2.

키워드