Reduced symplectic homology and string topology

Abstract

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 anti-symmetric 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.