  Using intersection theory in the context of Hilbert manifolds and geometric
homology we show how to recover the main operations of string topology built by
M. Chas and D. Sullivan. We also study and build an action of the homology of
reduced Sullivan's chord diagrams on the singular homology of free loop spaces,
extending previous results of R. Cohen and V. Godin and unifying part of the
rich algebraic structure of string topology as an algebra over the prop of
these reduced diagrams. Some of these operations are extended to spaces of maps
from a sphere to a compact manifold.
