I am at the beginning of my thesis work and I am trying to understand spectral triples. I can recall the definition but I have no informative examples with which to make sense of it. What are some examples I can keep in mind to help me put this definition in context?
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$\begingroup$ How comfortable are you with the commutative case? $\endgroup$– Yemon ChoiCommented Oct 4, 2018 at 8:53
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$\begingroup$ I am fairly new to the subject. Would the commutative case be spectral triples associated with C*-algebras that are algebras of continuous complex-valued functions on a compact Hausdorff space? $\endgroup$– TerryLCommented Oct 4, 2018 at 9:57
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2$\begingroup$ Yes - this was the starting point for Connes's definitions! I don't know where you are reading about spectral triples, but if they don't give some discussion of the case $C^\infty(M)$ then you need to find a source which does. A few minutes of Googling turns up e.g. this Master's thesis math.ru.nl/~landsman/Richard.pdf $\endgroup$– Yemon ChoiCommented Oct 4, 2018 at 11:11
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$\begingroup$ The setting in which I have seen spectral triples are in papers by Christiansen, Ivan, and Lapidus to obtain results on function spaces on fractals. $\endgroup$– TerryLCommented Oct 5, 2018 at 7:35
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