Bonn Topology Group - Abstracts

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April 9th 2019
Mark Powell (Durham University): The sphere embedding theorem.


Given an immersed sphere in a 4-manifold with self intersection number zero, when is it homotopic to a locally flat embedding? This question is central to the surgery and s-cobordism programme for classifying topological 4-manifolds. I will explain joint work with Arunima Ray and Peter Teichner, in which we prove a sphere embedding theorem. The statement is essentially contained in the Topology of 4-manifolds book of Freedman and Quinn, however the proof contains some gaps. One of these was discovered and remedied by Stong in the 90s. Another, relating to transverse spheres, was fixed by us. Transverse spheres are particularly important in applications of sphere embedding to surgery theory and the classification of 4-manifolds.

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