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Results tagged with vector-bundles
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user 22810
A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.
9
votes
1
answer
326
views
Closed formulas for topological K-theory?
Let $X$ be a compact manifold. I'm interested in whether any of the following cases admits a general closed formula for (complex)-$K$-theory. Let $E$ be a complex vector bundle with a given line bundl …
- 56.9k
7
votes
1
answer
2k
views
Tangent bundle of a homogeneous space and the euler exact sequence
Let $H \subset G$ be a closed subgroup of a lie group and $G/H$ the homogeneous coset space. There's an exact sequence of adjoint representations of $H$:
$$0 \to \mathfrak{h} \to \mathfrak{g} \to \ma …
- 1,624
6
votes
1
answer
2k
views
Transferring connection information to associated bundles and back
This might not be research level but I've tried more than once to ask about this in MSE and it got nowhere. So I thought It's fair to at least try.
At the risk of repeating well known stuff I tried t …
- 5,824
4
votes
2
answers
573
views
Principal bundles that can't be detected by spheres
The question I'm trying to answer is the following:
Let $P \to X$ be a principal $G$-bundle (over a connected CW complex)
satisfying that all pullbacks to spheres (of arbitrary dimension) are
…
- 43.2k
6
votes
4
answers
1k
views
What does "higher monodromy" tell us about a principal bundle
Let $P \to X$ be a principal $G-$bundle and let $f: X \to BG$ be its classifying map. As I understand there's some way to associate a monodromy representation $\pi_1(X) \to G$ to it. I know how to con …
- 118k