In this talk I will present recent results obtained in collaboration with Thomas Schick and
Vito Felice Zenobi.
The rho class of an invertible operator on a Galois $/Gamma$-covering is a very
interesting and useful secondary invariant. There are different equivalent definitions
of the rho class (Higson-Roe, Piazza-Schick, Xie-Yu, Zenobi) but in all of them the rho class is
a class in the K-theory of a suitable C^*-algebra. Work of Higson-Roe, Benameur-Roy
and Xie-Yu shows that the usual numeric rho invariants (the APS rho invariant, the
Cheeger-Gromov rho invariant and the Lott delocalised eta invariant) can be obtained from
the rho class by applying suitable traces.
In this talk I will address the problem of pairing the rho class class with higher cyclic cocycles,thus producing higher rho numbers.

海报