The Johnson homomorphism, embedding calculus and graph complexes
Quantum Algebra
2026-02-20 v2
Abstract
We explain how the Johnson homomorphism and the Enomoto-Satoh trace, as well as higher-loop-order generalizations, can be obtained from graph complexes originating in the Goodwillie-Weiss calculus. This paper can be seen as an addendum to our earlier work. It contains little new mathematical content, but is intended to give an overview of a different viewpoint on the Johnson homomorphism, for experts working mainly in the latter area.
Cite
@article{arxiv.2602.09915,
title = {The Johnson homomorphism, embedding calculus and graph complexes},
author = {Florian Naef and Thomas Willwacher},
journal= {arXiv preprint arXiv:2602.09915},
year = {2026}
}