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

Online availability

10.3842/SIGMA.2023.093

Library availability

Discover UIUC Full Text

Cite this

@article{69e87b354906462686ff45f1a72ff259,

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",

year = "2023",

doi = "10.3842/SIGMA.2023.093",

language = "English (US)",

volume = "19",

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

issn = "1815-0659",

publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

TY - JOUR

T1 - Vector Fields and Flows on Subcartesian Spaces

AU - Karshon, Yael

AU - Lerman, Eugene

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

UR - http://www.scopus.com/inward/record.url?scp=85177219228&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85177219228&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2023.093

DO - 10.3842/SIGMA.2023.093

M3 - Article

AN - SCOPUS:85177219228

SN - 1815-0659

VL - 19

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

Online availability

Library availability

Related links

Fingerprint

Cite this