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Results tagged with vector-bundles
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user 4008
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.
28
votes
Symmetric powers and duals of vector bundles in char p
I shall show that the answer is no when $p=2$ (and it seems to me that a
somewhat more involved calculation will work for any $p$). We shall show that
there exists a vector bundle $\mathcal E$ such th …
- 22.6k
15
votes
Accepted
Complex vector bundles with trivial Chern classes on k-tori
As the cohomology of $(S^1)^n$ is torsion free every stable bundle on $(S^1)^n$ is
determined by Chern classes (this also follows from the $K$-theory Künneth
formula) so just as for the spheres it is …
- 22.6k
12
votes
A ring such that all projectives are stably free but not all projectives are free?
This is an attempt to complete Tyler's argument. We first note that
$KO^0(S^5)=\mathbb Z$ (note this true for all spheres of dimension $\equiv 5,6,7 \bmod 8$). This means that every topological vector …
- 22.6k
7
votes
Deformations of sheaves via automorphisms. How to express $Ext^1$?
Here is a not so fancy description.
There is a general principle (in algebraic geometry but applicable to some
neighbouring disciplines) that says that anything that is functorial and
commutes with b …
- 22.6k