Boundary values of diffeomorphisms of simple polytopes, and controllability
Abstract
We consider the Lie group of smooth diffeomorphisms Diff$(M)$ of a simple polytope $M$ in the euclidean space. Simple polytopes are special cases of manifolds with corners. The geometric setting allows to study in particular, the subgroup of face respecting diffeomorphisms and its Lie theoretic properties. We find a canonical Lie group structure for the quotient of the diffeomorphism by the subgroup Diff$^{\partial,id}(M)$ of maps that equal the identity on the boundary, turning the canonical quotient homomorphism Diff$(M)\rightarrow $Diff$(M)/$Diff$^{\partial,id}(M)$ into a smooth submersion. We also show that the identity component of the diffeomorphism group is generated by the exponential image, by proving general controllability results.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Control and Dynamics of Mobile Robots
Quantum chaos and dynamical systems
Publication details
- Journal / source
- Differential Geometry and its Applications
- Publisher
- Elsevier BV
- Volume
- 104
- Pages
- 102404–102404
- Publication date
- 23 June 2026
- Language
- EN