This text is the extended version of a talk given at the conference Geometry,
Topology, QFT and Cosmology hold from May 28 to May 30, 2008 at the
Observatoire de Paris. We explore the notion of solder (or soldering form) in
differential geometry and propose an alternative interpretation of it,
motivated by the search of an accurate mathematical description of the General
Relativity. This new interpretation leads naturally to imagine a rich family of
new geometries which has not yet a satisfactory definition in general. We try
however to communicate to the reader an intuition of such geometries through
some examples and review quickly some possible applications in physics. The
basic objects in this geometry are not points (i.e. 0-dimensional), but
(p-1)-dimensional.Comment: in Geometry, Topology, QFT and Cosmology, Paris : France (2008
