The 4-dimensional disc embedding theorem and dual spheres
Abstract
We modify the proof of the disc embedding theorem for -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.
Keywords
Cite
@article{arxiv.2006.05209,
title = {The 4-dimensional disc embedding theorem and dual spheres},
author = {Mark Powell and Arunima Ray and Peter Teichner},
journal= {arXiv preprint arXiv:2006.05209},
year = {2025}
}
Comments
18 pages, 1 figure. v2: Added citations to Sato, removed previous Sec 9, added Rem 1.5. v3: Substantial rewrite of exposition; proofs unchanged, added details in Lemmas 4.1 and 4.2; added outline of our proof in Sec 1.2 and Rem 1.3 with alternative argument by referee; reordered so that disc embedding theorem proof comes first, then generic homotopies. This version to appear in Selecta Math