The computation of \(\eta\)-invariants on manifolds with free circle action (Q1577660)

In this paper the author considers a Riemannian spin-manifold \(M\) of positive scalar curvature carrying a free and isometric circle action of the circle \({\mathbf S}^1\) with geodesic orbits. He explicitly computes the \(\eta\)-invariant of twisted Dirac operators on \(M\), by a computation which is based upon the index theorem. As a first application he lists the explicit result for the (generalized) Berger spheres of dimension less than or equal to 11, and as a second application he derives a formula for the adiabatic limit of \(\eta\)-invariants.