K-theory and index formulas for boundary groupoid C*-algebras

TL;DR

This paper explicitly computes the K-groups of certain boundary groupoid C*-algebras with exponential isotropy subgroups and derives index formulas for elliptic pseudo-differential operators, linking K-theory and Fredholm indexes.

Contribution

It provides explicit K-theory computations and index formulas for boundary groupoid C*-algebras with exponential isotropy, advancing understanding of their operator theory.

Findings

Explicit K-group calculations for boundary groupoid C*-algebras

Derivation of index formulas for elliptic operators

Connection between K-theoretic and Fredholm indexes

Abstract

We compute explicitly the K-groups of some boundary groupoid C*-algebras with exponential isotropy subgroups. Then we derive index formulas that computes the K-theoretic and Fredholm indexes of elliptic (respectively totally elliptic) pseudo-differential operators on these groupoids.