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Exotic Sphere
CHF 43.15
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OB3CEC8ER6G
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Geliefert zwischen Mi., 28.01.2026 und Do., 29.01.2026
Details
In mathematics, an exotic sphere is a differentiable manifold that is homeomorphic to the standard Euclidean n-sphere, but not diffeomorphic. That means that such a manifold M is a sphere from a topological point of view, but not from the point of view of its differential structure. Thus, if M has dimension n, there is a homeomorphism h : M to S^n, but no such h is a diffeomorphism. The first exotic spheres were constructed by John Milnor (1956) in dimension n = 7 as S3-bundles over S4. He showed that there at least 7 differentiable structures on the 7-sphere. In any dimension Milnor (1959) showed that the diffeomorphism classes of oriented exotic spheres form the non-trivial elements of an abelian monoid under connected sum, which is a finite abelian group if the dimension is not 4. The classification of exotic spheres by Michel Kervaire and John Milnor (1963) showed that the oriented exotic 7-spheres are the non-trivial elements of a cyclic group of order 28 under the operation of connected sum.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130628970
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- EAN 9786130628970
- Format Fachbuch
- Titel Exotic Sphere
- Herausgeber Alphascript Publishing
- Anzahl Seiten 88
- Genre Mathematik
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