11. Note that \ textstyle i : N \ subset M need not be an embedded submanifold . 12. 1 ) The figure 8 is certainly not a submanifold of the plane, I agree. 13. Then, according to the implicit function theorem, the subspace of zeros of is a submanifold . 14. Examples of K�hler manifolds include smooth projective varieties and more generally any complex submanifold of a K�hler manifold. 15. By the implicit function theorem, every submanifold of Euclidean space is locally the graph of a function. 16. The Lagrangian Grassmannian is a submanifold of the ordinary Grassmannian of "'V " '. 17. When a complex manifold X is blown up along a submanifold Z, the blow up Hopf map. 18. If each is in the domain of a slice chart on in, then is an embedded submanifold . 19. That is, the submanifold topology on " S " is the same as the subspace topology. 20. SFT also associates a relative invariant of a Legendrian submanifold of a contact manifold known as relative contact homology.
