Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 19 (2023), 093, 17 pages      arXiv:2307.10959      https://doi.org/10.3842/SIGMA.2023.093

Vector Fields and Flows on Subcartesian Spaces

Yael Karshon ^ab and Eugene Lerman ^c
a) School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel
^b) Department of Mathematics, University of Toronto, Toronto, Ontario, Canada
^c) Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois, USA

Received July 21, 2023, in final form November 08, 2023; Published online November 16, 2023

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.

Key words: differential space; $C^\infty$-ring; subcartesian; flow.

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