Unknotting 2-dimensional spheres in S^4

Unknotting 2-dimensional spheres in S^4

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Maggie Miller, Princeton University
Fine Hall 110

In this talk, we discuss an interesting link between topology in dimensions 3 and 4. Scharlemann (1985) proved that a 2-sphere embedded in S^4 with 4 critical heights (an analog of bridge number from knot theory in S^3) is the boundary of a smooth 3-ball. We discuss a proof of this fact (Thompson, 1986) using 3-dimensional topology, and discuss other (open) unknotting conjectures for 2-spheres in S^4.