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Embedding calculus and
smooth structures
Ben Knudsen and Alexander Kupers |
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Geometry & Topology 28 (2024) 353–392
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Abstract |
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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 , 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
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Mathematical Subject Classification
Primary: 58D10
Secondary: 55P48, 57N35, 57R40
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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
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Authors |
| Ben Knudsen | |
| Department of Mathematics Northeastern University Boston, MA United States |
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| Alexander Kupers | |
| Department of Mathematics University of Toronto Toronto, ON Canada |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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