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Embedding Seifert fibered spaces in the 4-sphere

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Monday, February 04, 2019
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3:15 pm - 4:15 pm
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Ahmad Issa (University of Texas, Austin, Mathematics)
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Geometry/topology Seminar

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 an interesting conjecture which I'll discuss. This is joint work with Duncan McCoy.