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Vector Fields and Flows on Subcartesian Spaces
Yael Karshonab, Eugene Lermanc 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
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.
Keywords:
differential space, $C^\infty$-ring, subcartesian, flow.
Received: July 21, 2023; in final form November 8, 2023; Published online November 16, 2023
Citation:
Yael Karshon, Eugene Lerman, “Vector Fields and Flows on Subcartesian Spaces”, SIGMA, 19 (2023), 093, 17 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1988 https://www.mathnet.ru/eng/sigma/v19/p93
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