Embedding Seifert fibered spaces in the 4-sphere

Geometry Topology Seminar
Monday, April 1, 2019 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 006
Ahmad Issa – University of Texas, Austin
Jennifer Hom

Which 3-manifolds smoothly embed in the 4-sphere? This seemingly simple question turns out to be rather subtle. Using Donaldson's theorem, we derive strong restrictions to embedding a Seifert fibered space over an orientable base surface, which in particular gives a complete classification when e > k/2, where k is the number of exceptional fibers and e is the normalized central weight. Our results point towards a couple of interesting conjectures which I'll discuss. This is joint work with Duncan McCoy.