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Results tagged with vector-bundles
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user 16702
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.
3
votes
1
answer
2k
views
Linearization of a vector field
In a paper that I was reading, I stumbled across the following theorem:
Let $X$ be a vector field with $$X=
> a^ix^i\partial_{x^i} +
> \mathcal{O}(|x|^2),$$ where $x$ is
some chart and $a^i>0$. …
- 9,853
5
votes
0
answers
82
views
Vector bundles on space of germs
Let $X$ be the diffeological space of germs of paths $c: \mathbb{R} \rightarrow \mathbb{R}^n$, where two paths $c_1, c_2$ are equivalent if $c_1(t) = c_2(t)$ for all $t$ in some interval $(-\varepsilo …
- 9,853
3
votes
1
answer
436
views
Euler characteristics and the difference bundle construction
I am reading on K theory in Lawson and Michelson (Spin Geometry). One has the "exact sequence spaces" $L(X,Y)$ and there is the theorem that there is a unique equivalence of functors $\chi$ between $L …
- 9,853
3
votes
Does every vector bundle allow a finite trivialization cover?
I wonder that this was not said before.
Take a triangulation of your manifold. Choose disjoint open balls around each 0-cell in the triangulation and set the union to be $U_0$ (a ball means here some …
- 9,853