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.

arXiv comment34 pages

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Cited by in corpus (2)

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