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Results tagged with connections
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user 40297
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
Accepted
Question about a proof in Berthelot's crystalline book
Suppose you have a commutative ring $R$, a square zero ideal $I\subset R$, a $R$-module $M$ and an endomorphism $u$ of $M$ which is the identity modulo $IM$.
Then $v:= 1_M-u$ maps $M$ to $IM$, hence $ …
- 38k
29
votes
Manifolds admitting flat connections
For question 1 : if a vector bundle admits a flat connection, it comes from a representation of the fundamental group. Thus if $TM$ admits a flat connection and $M$ is simply-connected, $TM$ is trivi …
- 38k