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Results tagged with vector-bundles
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user 1708
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.
4
votes
Examples and properties of spaces with only trivial vector bundles
Here is another obstruction.
Suppose $M^n$ is a closed simply connected manifold which admits only trivial vector bundles. Then $M$ cannot be a $\mathbb{Z}/2\mathbb{Z}$-homology sphere, unless $n=3$ …
- 6,546
1
vote
Accepted
noncompact Riemannian homogeneous is trivial vector bundle over compact homogeneous
The only if direction fails. That is, there are $K$-equivariant vector bundles which are not homogeneous. For example, the Mobius band has the form $O(2)\times_{O(1)} \mathbb{R}$, and is not Riemann …
- 6,546