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Results tagged with fibre-bundles
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user 184
for questions about fiber bundles, including structure groups, principal bundles, and spaces of sections.
1
vote
Accepted
Locally trivial fibration over a suspension
It is independent of the choice of base point.
Let $Map((X,x_0), (G_F,id))$ be the based mapping space (based at $x_0$).
Let $Map(X, G_F)$ be the free mapping space. Then we have a split short exact …
- 27.5k
5
votes
Accepted
Can there exist two non-equivalent equivariant actions of a group on vector bundle?
Maybe I am miss understanding the question, but it seems the answer is yes.
Take your favorite G-space, mine is $S^1$ with the $\mathbb{Z}/2$-action "flip". Then consider the trivial vector bundles $ …
- 27.5k
6
votes
1
answer
716
views
Homomorphisms of Topological Groups which are Automatically Fiber Bundles?
Suppose I have a surjective homomorphism of topological groups $f:E \to G$. Let K be the kernel of f. The topological group K acts on E in an obvious way. When is this a fiber bundle over G? (It will …
- 27.5k
7
votes
Accepted
Critical points on a fiber bundle
The part I'm still hesitant about is that the manifold you call $C$ is $n$-dimensional. Codimension arguments in the infinite dimensional setting are always a little sticky. So, I'm just going to trea …
- 27.5k
5
votes
Accepted
Pull-back of a fibration along a homotopy equivalence and homotopy classes of sections
Here is one way of proving the conjecture is true in general, using the modern method of weak factorization systems.
A weak factorization system has at its core two classes of maps the left class an …
- 27.5k