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Embedding calculus for surfaces

Manuel Krannich and Alexander Kupers

Algebraic & Geometric Topology 24 (2024) 981–1018
Abstract

We prove convergence of the 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.

Keywords
embedding calculus, manifold calculus, surfaces, mapping class group, Johnson filtration
Mathematical Subject Classification
Primary: 58D10
Secondary: 57K20, 57R40, 57S05
References
Publication
Received: 17 December 2021
Revised: 21 September 2022
Accepted: 5 October 2022
Published: 12 April 2024
Authors
Manuel Krannich
Department of Mathematics
Karlsruhe Institute of Technology
Karlsruhe
Germany
Alexander Kupers
Department of Mathematics
University of Toronto
Toronto, ON
Canada

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