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Embedding calculus and smooth structures

Ben Knudsen and Alexander Kupers

Geometry & Topology 28 (2024) 353–392
Abstract

We study the dependence of the embedding calculus Taylor tower on the smooth structures of the source and target. We prove that embedding calculus does not distinguish exotic smooth structures in dimension 4, implying a negative answer to a question of Viro. In contrast, we show that embedding calculus does distinguish certain exotic spheres in higher dimensions. As a technical tool of independent interest, we prove an isotopy extension theorem for the limit of the embedding calculus tower, which we use to investigate several further examples.

Keywords
embedding calculus, smooth structures, $4$–manifolds
Mathematical Subject Classification
Primary: 58D10
Secondary: 55P48, 57N35, 57R40
References
Publication
Received: 12 July 2021
Revised: 10 March 2022
Accepted: 7 May 2022
Published: 27 February 2024
Proposed: Jesper Grodal
Seconded: Ulrike Tillmann, David Gabai
Authors
Ben Knudsen
Department of Mathematics
Northeastern University
Boston, MA
United States
Alexander Kupers
Department of Mathematics
University of Toronto
Toronto, ON
Canada

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