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<p>We modify the proof of the disc embedding theorem for 4-manifolds, which appeared as Theorem&#xa0;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.</p>

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The 4-dimensional disc embedding theorem and dual spheres

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月18日

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  • Mark Powell,
  • Arunima Ray,
  • Peter Teichner

摘要

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.