On diffeological principal bundles of non-formal pseudo-differential operators over formal ones

Abstract

We describe the structure of diffeological bundle of non formal classical pseudo-differential operators over formal ones, and its structure group. For this, we give results on diffeological principal bundles with (a priori) no local trivialization including an Ambrose-Singer theorem, use the smoothing connections alrealy exhibited by the author in previous works, and finish with open questions.

Keywords

• diffeology
• principal bundle
• pseudo-differential operators
• smoothnig operator
• index theory
• holonomy