Engel relations in 4-manifold topology

Michael Freedman; Vyacheslav Krushkal

Engel relations in 4-manifold topology

Geometric Topology 2018-07-30 v3 Group Theory

Authors: Michael Freedman , Vyacheslav Krushkal

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.

Keywords

Engel relations 4-manifold topology surgery conjecture A-B slice problem homotopy solution universal surgery problems homotopically trivial links double points

Cite

@article{arxiv.1412.5024,
  title  = {Engel relations in 4-manifold topology},
  author = {Michael Freedman and Vyacheslav Krushkal},
  journal= {arXiv preprint arXiv:1412.5024},
  year   = {2018}
}

Comments

53 pages. v3: Definition of weak link homotopy has been clarified and expanded (new section 6); other improvements in exposition

Engel relations in 4-manifold topology

Abstract

Keywords

Cite

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