The Universal η-Invariant for Manifolds With Boundary

bunke, ulrich;

We extend the theory of the universal η-invariant to the case of bordism groups of manifolds with boundaries. This allows the construction of secondary descendants of the universal η-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 η-invariants.