Vector Fields and Flows on Subcartesian Spaces

Yael Karshon; Eugene Lerman

doi:10.3842/SIGMA.2023.093

Vector Fields and Flows on Subcartesian Spaces

Yael Karshon
, Eugene Lerman

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English (US)
Article number	093
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	19
DOIs	https://doi.org/10.3842/SIGMA.2023.093
State	Published - 2023

Keywords

C-ring
differential space
flow
subcartesian

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2023.093

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title = "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.",

keywords = "C-ring, differential space, flow, subcartesian",

author = "Yael Karshon and Eugene Lerman",

note = "We thank Jordan Watts and Rui Fernandes for their help. Y.K.{\textquoteright}s research is partly funded by the Natural Science and Engineering Research Council of Canada and by the United States – Israel Binational Science Foundation. E.L.{\textquoteright}s research is partially supported by the Air Force Office of Scientific Research under award number FA9550-23-1-0337.",

year = "2023",

doi = "10.3842/SIGMA.2023.093",

language = "English (US)",

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journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

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AU - Karshon, Yael

AU - Lerman, Eugene

N1 - We thank Jordan Watts and Rui Fernandes for their help. Y.K.’s research is partly funded by the Natural Science and Engineering Research Council of Canada and by the United States – Israel Binational Science Foundation. E.L.’s research is partially supported by the Air Force Office of Scientific Research under award number FA9550-23-1-0337.

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - C-ring

KW - differential space

KW - flow

KW - subcartesian

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UR - https://www.scopus.com/pages/publications/85177219228#tab=citedBy

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DO - 10.3842/SIGMA.2023.093

M3 - Article

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

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

M1 - 093

ER -

Vector Fields and Flows on Subcartesian Spaces

Abstract

Keywords

ASJC Scopus subject areas

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