Homotopy versus isotopy: 2-spheres in 5-manifolds
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Date
2024-10
Publication Type
Journal Article
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Abstract
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 3. 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.
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published
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Volume
332 (2)
Pages / Article No.
195 - 218
Publisher
University of California
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Subject
homotopy implies isotopy; level preserving Whitney trick; metastable homotopy groups; Freedman-Quinn invariant; Dax invariant