n-transitivity of Bisection Groups of a Lie Groupoid

作者：Rybicki Tomasz^*

来源：Acta Mathematica Sinica-English Series, 2017, 33(8): 1061-1072.

DOI：10.1007/s10114-017-6125-3

• Lie groupoid
• bisection
• n-transitivity
• locality
• symplectic groupoid
• Lagrangian bisection

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 is an element of N by an arbitrary group of C-r-bisections of a Lie groupoid Gamma of class C-r, where 1 <= r <= omega, 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 Gamma is source connected for any arrow gamma is an element of Gamma, there is a bisection passing through gamma.

• 出版日期2017-8