Obstruction classes and Pontrjagin classes (Ex)
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− | Let $a_j = (3 - (-1)^j)/2$, let $k!$ be the integer k-factorial and | + | Let $a_j = (3 - (-1)^j)/2$, let $k!$ be the integer k-factorial and recall that $x \in H^{4i}(S^{4i})$ is a generator. |
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Revision as of 18:15, 17 March 2010
Contents |
1 Question
Take the stable vector bundle over the -sphere corresponding to a generator of . By defintion the the primary obstruction to trivialising is an obstruction class which generates .
Question 1.1.
What is the -th integral Pontryagin class of , ?
2 Answer
Let , let be the integer k-factorial and recall that is a generator.
Theorem 2.1 [Kervaire1959]. There is an identity
3 Further discussion
...
4 References
- [Kervaire1959] M. A. Kervaire, A note on obstructions and characteristic classes, Amer. J. Math. 81 (1959), 773–784. MR0107863 (21 #6585) Zbl 0124.16302