The universal eta-invariant for manifolds with boundary

Abstract

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.

36 pages (a number of mistakes corrected)

References in corpus (2)

• On the geometry of the f-invariant
• $MSp$ localized away from $2$ and odd formal group laws