Tweet at me your favorite differential operator and why you think it's better than the Hodge Laplacian
Would it not be more accurate to say that the Dirac operator is meaningless (i.e., undefined) until and unless a particular spin structure is specified? (Absolutely agree, of course, about the attractiveness of the notation.)
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If you changed "more accurate" to "true" I would agree whole-heartedly.
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Then would you please clarify what you meant when you said that the Dirac operator can distinguish between spin structures? Is it merely that the Dirac operator is, in a suitable sense, a one-to-one function of the spin structure?
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