The Exponential Decaying Noncommutative Differential Forms and Convolution Algebras

Abstract

We construct an algebra of rapidly decaying $C_0$ functions on an étale (Lie) groupoid, which extends the standard algebra of compactly supported noncommutative differential forms. In particular, using the theory of bisections, we prove that this algebra is closed under convolution. This construction clarifies the superconnection proof of Gorokhovsky and Lott.