A homotopy+ solution to the A-B slice problem
  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. 
Michael Freedman, Vyacheslav Krushkal
math.GT