Intrinsic Geometric Structure of Subcartesian Spaces

Richard Cushman; Jedrzej Sniatycki

doi:10.20944/preprints202311.1212.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 19 November 2023 / Approved: 20 November 2023 / Online: 20 November 2023 (05:29:43 CET)
Version 2 : Received: 25 November 2023 / Approved: 27 November 2023 / Online: 27 November 2023 (05:26:28 CET)

Every subset S of a Cartesian spaces Rd, endowed with differen- tial structure C∞(S) generated by restrictions to S of functions in C∞(Rd), has a canonical partition M(S) by manifolds, which are or- bits of the family X(S) of all derivations of C∞(S) that generate local one-parameter groups of local diffeomorphisms of S. This partition satisfies the frontier condition, Whitney’s conditions A and B. If M(S) is locally finite, then it satisfies all definitions of stratification of S. This result extends to Hausdorff locally Euclidean differential spaces.

subcartesian differential space
orbits of family of vector fields

Computer Science and Mathematics, Other

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Intrinsic Geometric Structure of Subcartesian Spaces

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