  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.
