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Results tagged with fibre-bundles
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user 40804
for questions about fiber bundles, including structure groups, principal bundles, and spaces of sections.
3
votes
Accepted
Reduction of the structure group of $\mathbb{R}^n$-fiber bundles to a special subgroup of $\...
Your group $G$ consists of homeomorphisms of $\Bbb R^n$ which induce homeomorphisms on $T^n$ with induced map $f_*: \pi_1(T^n) \to \pi_1(T^n)$ equal to the identity. (If $f$ satisfied $f(x+m) = f(x)+g …
- 9,580
9
votes
Classifying space of semidirect product of groups
I am adding my comment as an answer.
Every extension of groups $1 \to H \to G \to K \to 1$ corresponds to a fibration $$BH \to BG \to BK,$$ or a little more precisely at the space level $$EG/H \to (E …
- 9,580
2
votes
Accepted
Free $S^1$-action on compact homogeneous spaces
Here is a counterexample where $K$ is connected.
Let $W = SU_3/SO_3$ be the Wu manifold. This 5-dimensional manifold is simply-connected and has $H_2(W;\Bbb Z) = \Bbb Z/2$, and in particular, $\pi_2(W …
- 9,580