The 4-dimensional disc embedding theorem and dual spheres

Mark Powell; Arunima Ray; Peter Teichner

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arXiv · 2006.05209

The 4-dimensional disc embedding theorem and dual spheres

Mark Powell·Arunima Ray·Peter Teichner

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Abstract

We modify the proof of the disc embedding theorem for $4$-manifolds, which appeared as Theorem 5.1A in the book "Topology of 4-manifolds" by Freedman and Quinn, in order to construct geometrically dual spheres. These were claimed in the statement but not constructed in the proof. We also prove Proposition 1.6 from the Freedman-Quinn book regarding generic homotopies of discs or spheres in a 4-manifolds, which was not proven there.

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Mark Powell, Arunima Ray, Peter Teichner. 2020-06-09. The 4-dimensional disc embedding theorem and dual spheres. https://arxiv.org/abs/2006.05209

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