关于辛群胚的拉格朗日双截面

ON LAGRANGE BISECTIONS OF SYMPLECTIC GROUPOIDS

令 (Γ P ,α ,β)是辛群胚 .本文首先证明了K是Γ的拉格朗日双截面的充要条件 ,其次证明了一个关于Γ中拉格朗日双截面的存在性定理 .利用以上结果进而可以得到若K是Γ的拉格朗日双截面 ,则 (Γ K ,φ ,ψ)也是辛群胚 ,且与Γ辛群胚同构 ,最后给出拉格朗日双截面的具体例子 .

Let (ΓP,α,β) be a symplectic groupoid. We give first a necessary and sufficient condition of lagrange bisections. Then we prove a existence theorem for largrange bisections in Γ. Furthermore, using the results above we prove that (Γ K,φ,ψ ) is also a symplectic groupoid if K is a lagrange bisection in Γ. And it is isomorphism with (Γ P,α,β ). Last we give some examples of lagrange bisections.