In mathematics, more precisely in differential geometry, a soldering of a fiber bundle to a smooth manifold is a manner of attaching the fibers to the manifold in such a way that they can be regarded as tangent. Intuitively, soldering expresses in abstract terms the idea that a manifold may have a point of contact with a certain model Klein geometry at each point. In extrinsic differential geometry, the soldering is simply expressed by the tangency of the model space to the manifold. In intrinsic geometry, other techniques are needed to express it. Soldering was introduced in this general form by Charles Ehresmann in 1950.
Solder form of a circle over a torus.
Charles Ehresmann was a German-born French mathematician who worked in differential topology and category theory.
Charles Ehresmann (right) at the topology conference 1949 in Oberwolfach, together with Paul Vincensini (middle) and Georges Reeb (left)