Johnson Homomorphisms
Geometric Topology
2020-12-24 v3 Quantum Algebra
Abstract
This paper surveys work on generalized Johnson homomorphisms and tools for studying them. The goal is to unite several related threads in the literature and to clarify existing results and relationships among them using Hodge theory. We survey the work of Alekseev, Kawazumi, Kuno and Naef on the Goldman--Turaev Lie bialgebra, and the work of various authors on cohomological methods for determining the stable image of generalized Johnson homomorphisms. Various open problems and conjectures are included.
Keywords
Cite
@article{arxiv.1909.03914,
title = {Johnson Homomorphisms},
author = {Richard Hain},
journal= {arXiv preprint arXiv:1909.03914},
year = {2020}
}
Comments
Minor changes: the most significant were in section 11. To appear EMS Surveys