Exotic sphere
In mathematics, an exotic sphere is a differential manifold M, such that from a topological point of view M is a sphere, but not from the point of view of its differential structure. That is, if M has dimension n, there is a homeomorphism - h:M → Sn
but no such h is a diffeomorphism. The first exotic spheres were constructed by John Milnor in the case n = 7. They were -bundles over . This type of exotic sphere is called a Milnor sphere. Later techniques based on algebraic topology enable calculations of the numbers of distinct exotic spheres, in a given dimension. For dimension 7, there are 28 or 15 depending on whether the differential equivalence includes orientation or not.
|
|
