Andrew Hassell, Rafe Mazzeo and Richard B. Melrose
We present a signature formula for manifolds with corners of codimension two endowed with complete b-metrics. To prove it, we apply the results of our previous work on the limiting behaviour of the eta invariant under analytic surgery degeneration to the Atiyah-Patodi-Singer index theorem for an exhaustion by manifolds with boundary and examine the limiting behaviour. There is an extra contribution at the corners which is determined by the scattering data for the induced signature operator on the codimension one boundaries meeting at that corner. We also discuss some product formulas for the b-eta invariant.