What question did this study set out to answer?

This work aims to explore the properties of definable C^r groups and their subgroup actions in o-minimal expansions.

June 3, 2026Open Access

デファイナブルCʳ群と固有デファイナブル作用

Key Points

This work aims to explore the properties of definable C^r groups and their subgroup actions in o-minimal expansions.
Investigated the structure M as an o-minimal expansion of the real numbers.
Analyzed definable C^r groups and subgroups within the framework of C^ω and C^∞ cell decomposition.
Proved the existence of orbit maps for these groups.
Demonstrated that orbit maps exist under the conditions set by C^ω and C^∞ cell decomposition.
Established relationships between definable C^r groups and their subgroup actions.

Abstract

Let M= (R, +, ・, <,. . . ) be an o-minimal expansion of the standard structure R= (R, +, ・, <) of the field of real numbers. Let G be a definable Cʳ group and H a definable Cʳ subgroup of G. We prove that if M. admits the C^ω (resp. C^∞) cell decomposition or 0 ≤ r < ∞, then the orbit map π: G → G

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Tomohiro KAWAKAMI (Fri,) studied this question.

synapsesocial.com/papers/6a1fc616dee9eb8c0dce74ce https://doi.org/https://doi.org/10.19002/an00257977.58.9