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Results tagged with connections
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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
votes
1
answer
964
views
Is there a mathematical explanation for the Aharonov-Casher effect?
Recall that the Aharonov-Bohm effect can be interpreted mathematically as follows.
Consider an electromagnetic field A on some smooth manifold M, i.e., A is an element in the first differential cohom …
- 37.8k
15
votes
1
answer
1k
views
Are bundle gerbes bundles of algebras?
connection),
where vector bundles are defined
algebraically as dualizable modules over the algebra of smooth functions
or geometrically as vector spaces in the category of smooth submersions over M
and connections … For example, Corollary 4.9 in the paper by Urs Schreiber and Konrad Waldorf
Connections on non-abelian gerbes and their holonomy
proves that the bicategory of bundle gerbes with connection over M
is equivalent …
- 37.8k