Talk:Fibre homotopy trivial bundles (Ex)
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Given that $\pi_3(O_5)\to \pi_3(G_5)$ is isomorphic to the surjection $\mathbb Z\to \mathbb Z/24$, | Given that $\pi_3(O_5)\to \pi_3(G_5)$ is isomorphic to the surjection $\mathbb Z\to \mathbb Z/24$, | ||
we see that the vector bundle $\xi_k$ corresponding to $24k$ times the generator | we see that the vector bundle $\xi_k$ corresponding to $24k$ times the generator | ||
− | has a sphere bundle $S( | + | has a sphere bundle $S(\xi_k)$ which is fiber homotopically trivial, so in particular we have |
homotopy equivalences | homotopy equivalences | ||
</wikitex> | </wikitex> |
Revision as of 20:07, 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