$C^*$-algebras of $b$-pseudodifferential operators and an $\R^k$-equivariant index theorem

TL;DR

This paper computes K-theory invariants for algebras of pseudodifferential operators on manifolds with corners and establishes an R^k-equivariant index theorem, linking these results to the eta-invariant.

Contribution

It introduces new K-theory invariants for b-pseudodifferential operator algebras and proves an equivariant index theorem for R^k-invariant operators.

Findings

K-theory invariants of pseudodifferential operator algebras computed

An R^k-equivariant index theorem established

Relation between index theorem and eta-invariant discussed

Abstract

We compute $K$-theory invariants of algebras of pseudodifferential operators on manifolds with corners and prove an equivariant index theorem for operators invariant with respect to an action of $\R^k.$ We discuss the relation between our results and the $\eta$-invariant.