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According to Atiyah, a TQFT is a functor from the category of cobordisms to the category of vector spaces.

How does this definition relate with the physics of quantum mechanics?

What does the category of cobordism in the above definition represent physically?

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    To complement Qiachu Yuan's comment, in a TQFT you assign a Hilbert space to a manifold, the quantum Hilbert state space. Each cobordism represents a spacetime and the induced operator is time evolution. A TQFT is a toy model for quantum gravity. There are no local degrees of freedom and the theory can only keep track of changes in the topology, e.g. no metric or matter fields.2011-06-30
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    How does it create a model for quantum gravity?2011-07-01

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