Does anyone have an opinion on Rieffel's theory of compact quantum metric spaces? To me it seems to be a very interesting new area of mathematics. It shows how to generalise complicated geometric structures (which had not hitherto been considered) to the noncommutative setting, using really novel methods. However, it does not seem to have been taken on board by the noncommutative geometry community in general. For example, there are a huge number of questions to be answered about the theory's relationship with spectral triples. Can anyone account for the subject's neglect? Admittedly, the Rieffel's papers are nontrivial, but they are very well written and expository in spirit.
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closed as not constructive by Scott Morrison♦ Nov 11 '09 at 8:10
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