Functoriality for higher rho invariants of elliptic operators

Hao Guo  (Texas A&M University)

10:00-11:00, July 28, 2020   Zoom 514 693 6752

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.