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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 non-trivial, 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

As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, visit the help center for guidance.If this question can be reworded to fit the rules in the help center, please edit the question.

I agree it looks interesting - speaking only for myself, I am busy trying to keep my head above water and finish off existing projects. I'm surprised to hear it's (apparently) not received much attention from NCGers as a whole - hasn't Hangfeng Li done some stuff on this, or am I misremembering? – Yemon Choi Nov 10 '09 at 19:23
Hanfeng Li and David Kerr both worked in the area, but then they were both students of Rieffel. However, it may be that I have a wrong impression of how much attention it has received, if that's the case I'd like to be corrected. – John McCarthy Nov 10 '09 at 19:28
Oh, I'm not included in the NCG tent. I spend too much of my time thinking about commutative things (though in fairness sometimes they're non-cocommutative). Hopefully someone else can come along to tell us. – Yemon Choi Nov 10 '09 at 23:09
-1. This is a good discussion question, but a bad MO question. In particular, the answer to your question is "Yes, Rieffel has plenty of graduate students, and runs a weekly seminar." I've only attended said seminar occasionally, so all I can say about the second question is "Probably." – Theo Johnson-Freyd Nov 11 '09 at 0:57
Closed, per Theo's comment. – Scott Morrison Nov 11 '09 at 8:11