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MiS Preprint
31/2016

Differentiable stratified groupoids and a de Rham theorem for inertia spaces

Carla Farsi, Markus J. Pflaum and Christopher Seaton

Abstract

We introduce the notions of a differentiable groupoid and a differentiable stratified groupoid, generalizations of Lie groupoids in which the spaces of objects and arrows have the structures of differentiable spaces, respectively differentiable stratified spaces, compatible with the groupoid structure. After studying basic properties of these groupoids including Morita equivalence, we prove a de Rham theorem for locally contractible differentiable stratified groupoids. We then focus on the study of the inertia groupoid associated to a proper Lie groupoid. We show that the loop and the inertia space of a proper Lie groupoid can be endowed with a natural Whitney B stratification, which we call the orbit Cartan type stratification. Endowed with this stratification, the inertia groupoid of a proper Lie groupoid becomes a locally contractible differentiable stratified groupoid.

Received:
14.04.2016
Published:
15.04.2016

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2023 Repository Open Access
Carla Farsi, Markus J. Pflaum and Christopher Seaton

Differentiable stratified groupoids and a de Rham theorem for inertia spaces

In: Journal of geometry and physics, (2023)