Realizing the analytic surgery group of Higson and Roe geometrically, Part II: Relative eta-invariants

Abstract

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).

38 pages, to appear in Mathematische Annalen

References in corpus (4)

• Index, eta and rho-invariants on foliated bundles
• The Higson-Roe exact sequence and ${\ell }^2$ eta invariants
• Realizing the analytic surgery group of Higson and Roe geometrically, Part I: The geometric model
• Flat bundles, von Neumann algebras and $K$-theory with $\mathbb{R}/\mathbb{Z}$-coefficients

Cited by in corpus (1)

• The Higson-Roe exact sequence and ${\ell }^2$ eta invariants