• Speaker: Maggie Miller
• Time: 3:10-4:10
• Abstract: Often, interesting knotting vanishes when allowed one extra dimension, e.g. knotted circles in 3-space all become isotopic when included into 4-space. Hughes, Kim and I recently found a new counterexample to this principle: for g>1, there exists a pair of 3-dimensional genus-g solids in the 4-sphere with the same boundary, and that are homeomorphic relative to their boundary, but do not become isotopic rel boundary even when their interiors are pushed into the 5-dimensional ball. This proves a conjecture of Budney and Gabai (who previously constructed 3-balls in the 4-sphere with the same boundary that are not isotopic rel boundary) for g>1 in a very strong sense. In this talk, I’ll describe some interesting background theorems on codimension-2 knotting in higher dimensions and talk about related open problems in dimensions 3 and 4. This is joint work with Mark Hughes and Seungwon Kim.