Talk:Section (fiber bundle)

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[edit] Vector fields?

Suppose I have a particular vector field, over R². Is that a section of the tangent bundle of R²? —Ben FrantzDale 23:21, 28 April 2007 (UTC)

Yes. Vector fields are just sections of a vector bundle (usually the tangent bundle). -- Fropuff 01:32, 29 April 2007 (UTC)

Sweet. I'll add that to this page. Now sections make sense :-) —Ben FrantzDale 02:09, 29 April 2007 (UTC)

Regarding my edit: the set of all sections is not the bundle itself. Consider for example of a trivial line bundle over the real line. The space E is just R^2 and the base space is the x-axis. Sections of E are just continuous functions R → R represented as graphs. The space of all sections is just the space of all such functions, which is a different thing than the plane itself. -- Fropuff 02:28, 29 April 2007 (UTC)