The Johnson homomorphism, embedding calculus and graph complexes

TL;DR

This paper provides an overview of how the Johnson homomorphism and related traces can be derived from graph complexes within the framework of embedding calculus, offering a new perspective for experts.

Contribution

It offers a different viewpoint on the Johnson homomorphism by connecting it with graph complexes and embedding calculus, complementing previous work.

Findings

Johnson homomorphism derived from graph complexes

Enomoto-Satoh trace linked to Goodwillie-Weiss calculus

Higher-loop-order generalizations explained

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.