Talk:Fibre homotopy trivial bundles (Ex)
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We consider 5-dimensional real vector bundles over $S^4$. | We consider 5-dimensional real vector bundles over $S^4$. | ||
Isomorphism classes of these are given by their clutching function in $\pi_3(O_5)$ | Isomorphism classes of these are given by their clutching function in $\pi_3(O_5)$ |
Revision as of 20:03, 29 May 2012
We consider 5-dimensional real vector bundles over . Isomorphism classes of these are given by their clutching function in Given that is isomorphic to the surjection , we see that the vector bundle corresponding to times the generator has a sphere bundle which is fiber homotopically trivial, so in particular we have homotopy equivalences