The total Johnson homomorphism on the homology cylinder and the bracket-quantization HOMFLY-PT skein algebra
arXiv:2010.03764
Abstract
A homology cylinder of a surface induces an automorphism of the completed group ring of the fundamental group of the surface. We introduce a new method of computing the automorphism by using the Goldman Lie algebra of the surface or some skein algebra. In particular, we give a refinement of a formula by Kuno and Massuyeau.
54 pages, 21 figures