Controllability and diffeomorphism groups on manifolds with boundary
Peer reviewed, Journal article
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Date
2024Metadata
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- Institutt for matematiske fag [2604]
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Original version
10.1515/forum-2024-0160Abstract
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. Controllability and diffeomorphism groups on manifolds with boundary