vertical differential form
In differential geometry
Let be a bundle in the category Diff of smooth manifolds.
The dg-algebra of vertical differential forms on is the quotient of the de Rham complex dg-algebra of all forms on , by the dg-ideal of horizontal differential forms, hence of all those forms that vanish when any one vector in their arguments is a vertical vector field in that it is in the kernel of the differential .
For a trivial bundle the underlying complex of is .
Revised on June 10, 2014 02:29:29
by Urs Schreiber