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Results tagged with vector-bundles
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user 8032
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.
8
votes
1
answer
507
views
Weak Vector Bundles
The following notion has arisen in a paper I'm writing.
Definition. A map $p: E\to B$ of spaces
is said to be weak vector bundle if for all compact subspaces $K \subset B$
the restriction of $p$ to …
- 18.5k
4
votes
Accepted
Non-(stable)-triviality of the tautological bundles
For simplicity, let's take $\Bbb K = \Bbb R$.
By the bundle classification theorem, your question amounts to understanding whether the
inclusion map
$$
G_k(\Bbb R^N) \to \underset j{\text{colim }} \ …
- 18.5k
6
votes
Can one disjoin any submanifold in $\mathbb R^n$ from itself by a $C^{\infty}$-small isotopy?
There are lots of counter-examples.
Here's one:
The fibration $\text{SO}(3) \to \text{SO}(4) \to S^3$ splits, since it is the principal bundle of the tangent bundle of $S^3$, and the latter is paral …
- 18.5k
15
votes
Parallelizability of the Milnor's exotic spheres in dimension 7
The following is just an expansion of Johannes' last paragraph.
I went to Adams' paper where he attributes to Dold the statement that $S^n$ parallelizable implies $S^n$ is an $H$-space. No referenc …
- 18.5k