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I am applying for a short undergraduate/honours research project, and am trying to decide on preferences for a topic.

One of the possible topics is noncommutative geometry. I like the sound of this, however I haven't really been able to find a self-contained introduction to the area (and perhaps for good reason).

My question is twofold:

  1. How much commutative geometry, if any, would you say is necessary before jumping into the noncommutative side of things? (I am an undergraduate just finishing my third year of study and so don't really have any prior exposure to algebraic geometry.)
  2. Would anyone be able to recommend some "introductory" expositions in this area?

Thanks heaps :)

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    @JamesS.Cook Thanks for the references. I'm applying for a summer project meant to give 3rd (junior) year students exposure to research. I've done a substantial amount of abstract algebra (of the usual undergrad variety), but no algebraic/differential geometry.2012-08-29

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