• Corpus ID: 219558930

The 4-dimensional disc embedding theorem and dual spheres

@article{Powell2020The4D,
  title={The 4-dimensional disc embedding theorem and dual spheres},
  author={Mark Powell and Arunima Ray and Peter Teichner},
  journal={arXiv: Geometric Topology},
  year={2020}
}

• Mark Powell, Arunima Ray, P. Teichner
• Published 9 June 2020
• Mathematics
• arXiv: Geometric Topology

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.
Fundamental results in 4-manifold topology such as the existence and exactness of the surgery sequence, the s-cobordism theorem, and thence the classification of closed, simply connected topological 4-manifolds up to homeomorphism, rely on a closely related sphere embedding theorem with geometrically dual spheres, which is proven using the disc embedding theorem. We give an example to show that geometrically dual spheres are essential in applications.