Abstract

I will report on joint work with Zhizhang Xie and Guoliang Yu on functoriality properties of
the higher rho invariant of elliptic differential operators on manifolds with symmetry.
More precisely, given a map between two Galois covers of a closed spin manifold,
one of which is a quotient of the other, we give a geometric proof that the induced map
on the level of (maximal) geometric C*-algebras naturally relates the higher indices
and higher rho invariants of the lifted Dirac operators on the two covers.
Recently, this result was used by Wang-Xie-Yu to compute higher rho invariants on covering spaces
by relating them to higher invariants on finite-sheeted covers.