Solder form
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In mathematics, more precisely in differential geometry, a solder form on a smooth principal G-bundle over a smooth manifold M is a horizontal and G-equivariant differential 1-form on P with values in a linear representation V of G such that the associated bundle map from the tangent bundle TM to the associated bundle P×G V is a bundle isomorphism. (In particular, V and M must have the same dimension.) The associated bundle isomorphism is also sometimes called a solder form.
A motivating example of a solder form is the tautological or fundamental form on the frame bundle of a manifold.
The reason for the name is that a solder form solders (or attaches) the abstract principal bundle to the manifold M by identifying an associated bundle with the tangent bundle. Solder forms provide a method for studying G-structures and are important in the theory of Cartan connections. The terminology and approach is particularly popular in the physics literature.
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