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