<Emphasis Type="Italic">n</Emphasis>-transitivity of bisection groups of a Lie groupoid |
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Authors: | Tomasz Rybicki |
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Institution: | AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Kraków, Poland |
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Abstract: | The notion of n-transitivity can be carried over from groups of diffeomorphisms on a manifold M to groups of bisections of a Lie groupoid over M. The main theorem states that the n-transitivity is fulfilled for all n ∈ N by an arbitrary group of Cr-bisections of a Lie groupoid Γ of class Cr, where 1 ≤ r ≤ ω, under mild conditions. For instance, the group of all bisections of any Lie groupoid and the group of all Lagrangian bisections of any symplectic groupoid are n-transitive in the sense of this theorem. In particular, if Γ is source connected for any arrow γ ∈ Γ, there is a bisection passing through γ. |
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Keywords: | Lie groupoid bisection n-transitivity locality symplectic groupoid Lagrangian bisection |
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