THE UNIVERSAL -INVARIANT FOR MANIFOLDS WITH BOUNDARY

Abstract

We extend the theory of the universal eta-invariant to the case of bordism groups of manifolds with boundaries. This allows the construction of secondary descendants of the universal eta-invariant. We obtain an interpretation of Laures' f-invariant as an example of this general construction. As an aside, we improve a recent result by Han-Zhang about the modularity of a certain formal power series of eta-invariants.