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Homotopy versus
isotopy: 2-spheres in 5-manifolds
Danica Kosanović, Rob Schneiderman and Peter Teichner |
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Vol. 332 (2024), No. 2, 195–218
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Abstract |
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We give a complete obstruction for two homotopic embeddings of a 2-sphere into a 5-manifold to be isotopic. The results are new even though the methods are classical, the main tool being the elimination of double points via a level preserving Whitney move in codimension . Moreover, we discuss how this recovers a particular case of a result of Dax on metastable homotopy groups of embedding spaces. It follows that “homotopy implies isotopy” for 2-spheres in simply connected 5-manifolds and for 2-spheres admitting algebraic dual 3-spheres. |
Keywords
2-spheres in 5-manifolds, homotopy implies isotopy, level
preserving Whitney trick, metastable homotopy groups,
Freedman–Quinn invariant, Dax invariant
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Mathematical Subject Classification
Primary: 57K45, 57R40, 58D10
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Milestones
Received: 11 April 2024
Revised: 9 July 2024
Accepted: 21 September 2024
Published: 6 December 2024
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Authors |
| Danica Kosanović | |
| Department of Mathematics ETH Zürich Zürich Switzerland |
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| Rob Schneiderman | |
| Department of Mathematics Lehman College City University of New York Bronx, NY United States |
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| Peter Teichner | |
| Max-Planck-Institut für
Mathematik Bonn Germany |
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| © 2024 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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