Smooth Homotopy 4-Sphere
It is shown that every homotopy 4-disk with boundary 3-sphere is diffeomorphic to the 4-disk, so that every smooth homotopy 4-sphere is diffeomorphic to the 4-sphere. As a consequence, it is also shown that any (smoothly) embedded 3-sphere in the 4-sphere splits the 4-sphere into two components of 4...
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Veröffentlicht in: | WSEAS Transactions Mathematics 2023-09, Vol.22, p.690-701 |
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Format: | Artikel |
Sprache: | eng |
Online-Zugang: | Volltext |
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Zusammenfassung: | It is shown that every homotopy 4-disk with boundary 3-sphere is diffeomorphic to the 4-disk, so that every smooth homotopy 4-sphere is diffeomorphic to the 4-sphere. As a consequence, it is also shown that any (smoothly) embedded 3-sphere in the 4-sphere splits the 4-sphere into two components of 4-manifolds which are both diffeomorphic to the 4-ball. The argument used for the proof also shows that any two homotopic diffeomorphisms of the stable 4-sphere are smoothly isotopic if one diffeomorphism allows a local diffeomorphism change, so that they are smoothly concordant and piecewise-linearly isotopic. |
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ISSN: | 1109-2769 2224-2880 |
DOI: | 10.37394/23206.2023.22.76 |