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Results tagged with fibre-bundles
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user 1708
for questions about fiber bundles, including structure groups, principal bundles, and spaces of sections.
25
votes
1
answer
1k
views
When are fiber bundles reversible?
My question, in its most general form is this:
Given a fiber bundle $F\rightarrow E\rightarrow B$, when is there a fiber bundle $B\rightarrow E\rightarrow F$?
Here, F,E, and B can lie in whichev …
- 6,546
24
votes
1
answer
3k
views
Characteristic classes of sphere bundles over spheres in terms of clutching functions
I'm trying to understand Milnor's proof of the existence of exotic 7-spheres.
Milnor finds his examples among $S^{3}$ bundles over $S^{4}$ (with structure group $SO(4)$ ). Such a bundle can be descr …
- 6,546
19
votes
2
answers
1k
views
What manifold has $\mathbb{H}P^{odd}$ as a boundary?
This question is motivated by What manifolds are bounded by RP^odd? (as well as a question a fellow grad student asked me) but I can't seem to generalize any of the provided answers to this setting.
…
- 6,546
3
votes
Accepted
Cohomogeneity one action on $S^7$-bundles over $S^8$
I don't think the argument is written down anywhere, but not all $S^7$-bundles over $S^8$ admit cohomogeneity one actions.
Focusing on those with Euler class $\pm 1$, the resulting total space $E$ is …
- 6,546