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Results tagged with connections
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user 4177
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].
9
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0
answers
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Is there a contact instanton connection on the tangent bundle of the 5-sphere?
It is not clear at all if there are connections on $TS^5$ that satisfy $(1)$ for any $g$, or for that matter, any combination of $g$ and $\eta$ (I guess we should ask for a contact metric structure, to …
- 35.5k
9
votes
1
answer
488
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How algebraic is the holonomy map?
Consider the space $\mathcal{A}$ of polynomial or Laurent connections (again, take the option that works or makes sense) on the trivial $G$-bundle on $\mathbb{C}^\times$. … In the case of smooth connections on $G\times S^1$ (and probably for analytic too) we have a holonomy map $\mathcal{A}^{sm} \to G$, and this is a surjective submersion. …
- 45.7k