The universal eta-invariant for manifolds with boundary

Understand

We extend the theory of the universal eta-invariant to the case of relative 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 of Han-Zhang on the modularity of a certain power series of eta invariants.