Fibre homotopy trivial bundles (Ex)
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Revision as of 19:29, 29 May 2012 by Martin Olbermann
- Observe that classifies -spherical fibrations over . Using the isomorphisms , and the fact that the J-homomophism in dimension is isomorphic to the surjective homomorphism , find a homotopy equivalence of manifolds such that . Here denotes the total Pontrjagin class.
- The above exercise showed that the first Pontrjain class, , is not a homotopy invariant. Apply the same idea to show that is not a homotopy invariant for any .
Remark 0.2. A reference to Novikov is needed here.