... freedom1
It would be nicely symmetrical if TQFTs involved the constants and but not . Unfortunately I cannot quite see how to make this idea precise.
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... time2
Here and in what follows, by `manifold' I really mean `compact oriented smooth manifold', and cobordisms between these will also be compact, oriented, and smooth.
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... changes3
Actually, while perfectly correct as far as it goes, this resolution dodges an important issue. Some physicists have suggested that the second axiom may hold even in quantum field theories with local degrees of freedom, so long as they are background-free [10]. Unfortunately a discussion of this would take us too far afield here.
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