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Results tagged with connections
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user 13647
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].
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comparison theorem for connections with regular singularities
The morphism $\mathbb{H}^*(X,DR(\mathcal{F},\nabla))\rightarrow \mathbb{H}^*(X^\mathrm{an},DR(\mathcal{F}^\mathrm{an},\nabla^\mathrm{an}))$ is always an isomorphism when $\mathcal{F}$ is regular. This …
- 1,838
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regular singularities
We can see what $\ker(\nabla^\mathrm{an})$ will be by the following reasoning (which can be made a bit more precise):
$\nabla(f)=0\Leftrightarrow \frac{df}{f}=-\alpha\frac{dt}{t}\Leftrightarrow \log( …
- 1,838