Geodesic
ENGEL RELATIONS IN 4-MANIFOLD TOPOLOGY
Forum of Mathematics, Sigma, Tome 4 (2016)

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We give two applications of the 2-Engel relation, classically studied in finite and Lie groups, to the 4-dimensional (4D) 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. 
@article{10_1017_fms_2016_20,
     author = {MICHAEL FREEDMAN and VYACHESLAV KRUSHKAL},
     title = {ENGEL {RELATIONS} {IN} {4-MANIFOLD} {TOPOLOGY}},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {4},
     year = {2016},
     doi = {10.1017/fms.2016.20},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2016.20/}
}
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MICHAEL FREEDMAN; VYACHESLAV KRUSHKAL. ENGEL RELATIONS IN 4-MANIFOLD TOPOLOGY. Forum of Mathematics, Sigma, Tome 4 (2016). doi: 10.1017/fms.2016.20

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