Work

The 4-dimensional disc embedding theorem and dual spheres

Year: 2025

Type: article

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.

Source: Selecta Mathematica

DOI: 10.1007/s00029-025-01069-y

Authors: Mark Powell, Arunima Ray, Peter Teichner

Institutions: University of Glasgow, Max Planck Institute for Mathematics

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Durham University, Hausdorff Center for Mathematics, Engineering and Physical Sciences Research Council