Realizing the analytic surgery group of Higson and Roe geometrically,   Part II: Relative eta-invariants
  We apply the geometric analog of the analytic surgery group of Higson and Roe to the relative $\eta$-invariant. In particular, by solving a Baum-Douglas type index problem, we give a "geometric" proof of a result of Keswani regarding the homotopy invariance of relative $\eta$-invariants. The starting point for this work is our previous constructions in "Realizing the analytic surgery group of Higson and Roe geometrically, Part I: The geometric model" (arXiv:1308.5990). 
Robin Deeley, Magnus Goffeng
math.KT math.OA