We introduce a common domain of definition for the loop product and the loop
coproduct, reduced loop homology, on which they combine to a unital infinitesimal
antisymmetric bialgebra structure. In particular, a relation conjectured by Sullivan
holds with an extra term. The structure depends on choices governed by secondary
continuation maps. These results on string topology are proved in the more general
context of reduced symplectic homology for a suitable class of Weinstein
manifolds.
