Vector Fields and Flows on Subcartesian Spaces

Author:

Yael Karshon, Eugene Lerman

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Symplectic Geometry (math.SG)

journal:

SIGMA 19 (2023), 093, 17 pages

date:

2023-07-19 16:00:00

Abstract

This paper is part of a series of papers on differential geometry of $C^\infty$-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 $C^\infty$-ring of global smooth functions integrate to smooth flows.

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