2:00 pm Wednesday, March 7, 2018
Junior Topology: Embedding Seifert fibered spaces in the 4-sphere by Ahmad Issa in RLM 12.166
Which 3-manifolds smoothly embed in the 4-sphere? This seemingly simple question turns out to be surprisingly subtle and difficult. In this talk, we restrict to the case of Seifert fibered 3-manifolds over an arbitrary oriented base surface F. Such a space M, with non-zero generalised Euler invariant, is determined by (F; e; r_1, ..., r_k) where e is a positive integer and r_1,...,r_k are rationals larger than 1 (here we've oriented M to bound a positive definite plumbing). For e at least k/2, we determine precisely which M pass a powerful obstruction to embedding based on Donaldson's theorem, and then attempt to either embed M or apply further obstructions in those cases. For e greater than k/2, this gives a complete determination of which such M embed. This is joint work with Duncan McCoy. Submitted by
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