Embedding calculus for surfaces

TL;DR

This paper proves the convergence of embedding calculus for surfaces, including diffeomorphisms, and connects the Johnson filtration of the surface's mapping class group to an embedding calculus filtration.

Contribution

It establishes convergence results for embedding calculus in low dimensions and links it to the Johnson filtration of the mapping class group.

Findings

Embedding calculus converges for surfaces and their diffeomorphism spaces.

A relationship is established between the Johnson filtration and an embedding calculus filtration.

The results apply specifically to manifolds of dimension at most two.

Abstract

We prove convergence of Goodwillie-Weiss' embedding calculus for spaces of embeddings into a manifold of dimension at most two, so in particular for diffeomorphisms between surfaces. We also relate the Johnson filtration of the mapping class group of a surface to a certain filtration arising from embedding calculus.