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Possible duplicate: What is the significance of non-commutative geometry in mathematics?

Hi, I've read some introductory articles and lecture notes on (Connes) noncommutative geometry that generalizes Riemannian geometry. I was wondering whether there are any benifits/results in the back direction, i.e. Results in Riemannian geometry that are obtained by methods in noncommutative geometry? Thanks in advance.

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  • $\begingroup$ See this question: mathoverflow.net/questions/88184/… for some examples. There are lots of applications to foliations and index theory, to name just two examples. Also, in a slightly different vein, the rational injectivity of the assembly map (keyword: Baum-Connes conjecture) implies the Novikov conjecture. $\endgroup$ – MTS May 25 '12 at 21:01
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    $\begingroup$ In fact, I am voting to close this question as a duplicate of the one I linked to. $\endgroup$ – MTS May 25 '12 at 21:35

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