A homotopy+ solution to the A-B slice problem
Michael Freedman, Vyacheslav Krushkal
TL;DR
This paper introduces a new approach to the A-B slice problem, a key aspect of the 4-dimensional topological surgery conjecture, by employing a link-homotopy+ solution based on the 2-Engel relation.
Contribution
It provides the first link-homotopy+ solution to the A-B slice problem using geometric methods related to the 2-Engel relation.
Findings
The A-B slice problem admits a link-homotopy+ solution.
Implications for the 4D surgery conjecture are discussed.
Geometric applications of the 2-Engel relation are crucial to the proof.
Abstract
The A-B slice problem, a reformulation of the 4-dimensional topological surgery conjecture for free groups, is shown to admit a link-homotopy+ solution. The proof relies on geometric applications of the group-theoretic 2-Engel relation. Implications for the surgery conjecture are discussed.
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