Engel relations in 4-manifold topology

Michael Freedman; Vyacheslav Krushkal

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arXiv · 1412.5024

Engel relations in 4-manifold topology

Michael Freedman·Vyacheslav Krushkal

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Abstract

We give two applications of the 2-Engel relation, classically studied in finite and Lie groups, to the 4-dimensional topological surgery conjecture. The A-B slice problem, a reformulation of the surgery conjecture for free groups, is shown to admit a homotopy solution. We also exhibit a new collection of universal surgery problems, defined using ramifications of homotopically trivial links. More generally we show how n-Engel relations arise from higher order double points of surfaces in 4-space.

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BibTeX RIS

Michael Freedman, Vyacheslav Krushkal. 2014-12-16. Engel relations in 4-manifold topology. https://arxiv.org/abs/1412.5024

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