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### Relation between nCob and Hilb

Given the category nCob and Hilb, it is possible to create a covariant functor such that, for any (n-1)-manifold S it assigns a Hilbert space of states Z(S) and, given a cobordism we obtain the corresponding function .Z(M) is such that the following conditions are satisfied:

- given
and
then

- where S=(n-1)-dimensional manifold.

J. Baez identified this functor as a representation of a Topological Field Theory (For details see [1])

Cecilia Flori 2006-11-21