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arXiv · 2403.12742

Controllability and diffeomorphism groups on manifolds with boundary

Erlend Grong·Alexander Schmeding
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Abstract

In this article we consider diffeomorphism groups of manifolds with smooth boundary. We show that the diffeomorphism groups of the manifold and its boundary fit into a short exact sequence which admits local sections. In other words, they form an infinite-dimensional fibre bundle. Manifolds with boundary are of interest in numerical analysis and with a view towards applications in machine learning we establish controllability results for families of vector fields. This generalises older results due to Agrachev and Caponigro in the boundary-less case. Our results show in particular that the diffeomorphism group of a manifold with smooth boundary is generated by the image of the exponential map.

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Erlend Grong, Alexander Schmeding. 2024-03-19. Controllability and diffeomorphism groups on manifolds with boundary. https://doi.org/10.1515/forum-2024-0160

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