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Results tagged with connections
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user 154157
Ehresmann connections; covariant derivatives; connections on vector bundles, principal bundles, ∞-bundles, submersions, bundle gerbes; holonomy and higher holonomy; parallel transport; torsion; curvature. See also the tags [principal-bundles], [vector-bundles], [gerbes], [curvature], [geodesics], [characteristic-classes], [torsion].
10
votes
2
answers
2k
views
When do flat holomorphic connections exist?
I know from How many flat connections has a line bundle in algebraic geometry? …
- 3,720
6
votes
1
answer
462
views
What exactly is the relationship between an Ehresmann connection and splitting of the jet se...
In algebraic geometry, I am familiar with the equivalence between connections on a locally free sheaf $\mathcal{E}$ and splitting of the sequence
$$ 0 \to \Omega_X^1 \otimes \mathcal{E} \to J^1(\mathcal …
- 3,720
2
votes
1
answer
152
views
Splitting of higher order jet sequence
Let $X$ be a smooth variety. Because $\mathcal{O}_X$ admits a canonical connection $\mathrm{d} : \mathcal{O}_X \to \Omega_X$ the sequence,
$$ 0 \to \Omega_X \to J^1(\mathcal{O}_X) \to \mathcal{O}_X \t …
- 3,720