On the n-transitivity of the group of equivariant diffeomorphisms

2024/07/17 by Marja Kankaanrinta, Kankaanrinta, Marja
Mathematics · #57S20 57R18 57S05 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2407.12510

openalex publication_date 2024/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a Lie group and let M be a proper smooth G-manifold. If M is connected and dim(M)≥ 2, the group of diffeomorphisms of M, that are isotopic to the identity through a compactly supported isotopy, acts n-transitively on M, for any n. In this paper, we prove a version of the n-transitivity result for the group of equivariant diffeomorphisms of M. As a corollary we obtain a result concerning diffeomorphisms of the orbit space M/G. A special case of the result for orbit spaces gives an n-transitivity result for orbifold diffeomorphisms that was earlier proved by F. Pasquotto and T. O. Rot.

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