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Results tagged with vector-bundles
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user 2625
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.
5
votes
3
answers
2k
views
The correspondence between affine vector bundles and f.g. projective modules
The definition of a (geometric) vector bundle over a scheme $X$ can be rewritten as follows in terms of 'not-so-geometrical algebra' if $X=Spec R$ is affine and if I am not missing something.
A vecto …
- 2,782
16
votes
4
answers
1k
views
Algebraic analogue of the Moebius bundle over the circle
Let $R$ be the ring $R[X,Y]/(X^2+Y^2−1)$. The space of $\mathbb{R}$-rational points of the affine scheme associated to $R$ is the topological circle $S^1$.
An algebraic vector bundle over $R$ is an $ …
- 2,782
8
votes
2
answers
481
views
Swan-like theorem and covering spaces
Let $X$ be a finite CW complex. Swan's theorem provide an equivalence
$$
{\rm Vec}(X)\xrightarrow\sim{\rm ProjMod}(\mathop{\rm hom}\nolimits_{\rm Top}(X,\mathbb{R}))
$$
between the category of finite …
- 2,782