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Results tagged with vector-bundles
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user 2039
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
Analogy between Stiefel-Whitney and Chern classes
Let me try a high-brow answer using equivariant stable homotopy theory.
By the stable Thom isomorphism, the integral (co)homology of $BU$ agrees with that of $MU$; likewise the $\mathbb{Z}/2$-(co)ho …
- 12.1k
8
votes
1
answer
1k
views
Vector bundles on open (affine) curves
It is well-known by Grothendieck (or earlier by Dedekind-Weber) that every vector bundle on $\mathbb{P}^1_k$ for $k$ a field decomposes into a sum of the line bundles $\mathcal{O}(k)$.
As investigated …
- 12.1k