# Talk:Kernel formation (Ex)

From Manifold Atlas

The lens space is a union of two solid tori glued along the boundary. The gluing diffeomorphism is such that , where and denote the longtitude and meridian of the solid torus. From this Heegard decomposition we obtain the kernel formation

The first lagrangian is spanned by the generator of . This generator is exactly the meridian . The same argument shows, that the second lagrangian is generated by the image of the meridian of complementary torus . Certainly we have . Furthermore it is easy to see that the index of in is equal to . Thus the kernel formation is trivial if and only if . We have , thus we obtain trivial formations for :

For it is sufficient to notice that . Thus the associated formation is: