n-transitivity of Bisection Groups of a Lie Groupoid  

作　　者：Tomasz RYBICKI 

机构地区：[1]AGH University of Science and Technology,Faculty of Applied Mathematics,al.Mickiewicza 30,30-059 Krakdw,Poland

出　　处：《Acta Mathematica Sinica,English Series》2017年第8期1061-1072,共12页数学学报（英文版）

基　　金：Partially supported by AGH grant n.11.420.40

摘　　要：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 F 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 F is source connected for any arrow γ∈ Г, there is a bisection passing through γ.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 F 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 F is source connected for any arrow γ∈ Г, there is a bisection passing through γ.

关 键 词：Lie groupoid BISECTION n-transitivity LOCALITY symplectic groupoid Lagrangian bisection 

分 类 号：O152.5[理学—数学]