  The rho-invariant is an invariant of odd-dimensional manifolds with finite
fundamental group, and lies in the representations modulo the regular
representations (after tensoring with Q). It is a fundamental invariant that
occurs in classifying lens spaces, their homotopy analogues, and is intimately
related to the eta-invariant for the signature operator. The goal of this note
is to use some of the technology developed in studying the Novikov higher
signature conjecture to define an analogous invariant for certain situations
with infinite fundamental group.
