Vector Fields and Flows on Subcartesian Spaces

Abstract

This paper is part of a series of papers on differential geometry of 𝐶∞-ringed spaces. In this paper, we study vector fields and their flows on a class of singular spaces. Our class includes arbitrary subspaces of manifolds, as well as symplectic and contact quotients by actions of compact Lie groups. We show that derivations of the 𝐶∞-ring of global smooth functions integrate to smooth flows.