The 4-dimensional disc embedding theorem and dual spheres

• Mark Powell ^[1] ; Arunima Ray ^[2] ; Peter Teichner ^[2]
  1. [1] University of Glasgow

     University of Glasgow

     Reino Unido

     
  2. [2] Max Planck Institute for Mathematics

     Max Planck Institute for Mathematics

     Kreisfreie Stadt Bonn, Alemania

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 31, Nº. 4, 2025
• Idioma: inglés
• DOI: 10.1007/s00029-025-01069-y
• Enlaces
  • Texto completo
• Resumen

  • 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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