Functoriality for higher rho invariants of elliptic operators

Abstract

Let $N$ be a closed spin manifold with positive scalar curvature and $D_N$ the Dirac operator on $N$. Let $M_1$ and $M_2$ be two Galois covers of $N$ such that $M_2$ is a quotient of $M_1$. Then the quotient map from $M_1$ to $M_2$ naturally induces maps between the geometric $C^{\ast }$-algebras associated to the two manifolds. We prove, by a finite-propagation argument, that the \emph{maximal} higher rho invariants of the lifts of $D_N$ to $M_1$ and $M_2$ behave functorially with respect to the above quotient map. This can be applied to the computation of higher rho invariants, along with other related invariants.

34 pages

References in corpus (4)

• Higher Orbit Integrals, Cyclic Cocyles, and K-theory of Reduced Group C*-algebra
• Coarse geometry and Callias quantisation
• Positive scalar curvature and an equivariant Callias-type index theorem for proper actions
• Approximations of delocalized eta invariants by their finite analogues

Cited by in corpus (2)

• Approximations of delocalized eta invariants by their finite analogues
• Interior Kasparov product for $\varrho$-classes on Riemannian foliated bundles