A regular homotopy version of the Goldman-Turaev Lie bialgebra, the   Enomoto-Satoh traces and the divergence cocycle in the Kashiwara-Vergne   problem
  By introducing a refinement of the Goldman-Turaev Lie bialgebra, we interpret the divergence cocycle in the Kashiwara-Vergne problem and the Enomoto-Satoh obstructions for the surjectivity of the Johnson homomorphisms as some part of a regular homotopy version of the Turaev cobracket. 
Nariya Kawazumi
math.GT