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I want to try to understand non commutative geometry by reading Connes's book ..and I am discovering it is a hard book to read :-) as I miss a lot of background specially in operator algebra and homology theory ( my field is nonlinear PDE so I know a bit of functional analysis already- at least the one used in my field).

So my question: what reading could be recommended in order to prepare a non expert mathematician to read Connes's book? For example, there are so many book on operator algebra or homology theory ...and my personal pick will be random, so I am seeking for expert recommendations:

Thanks in advance JF

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  • $\begingroup$ Do you know some differential geometry? $\endgroup$ – Yemon Choi Dec 29 '17 at 16:59
  • $\begingroup$ yes basic riemanian geometry @undergraduate level $\endgroup$ – JeffInVermont Dec 29 '17 at 17:23
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To understand everything in Connes' book you would need expertise in many different fields. My advice would be to browse it and see if anything attracts your interest. Then you can read up on the relevant background for that topic.

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    $\begingroup$ I had a similar experience with Connes's book when I was an undergrad. It bewildered me beyond anything I had read on math before, also because it was (and probably still is) way above my head. However, I did realize then I would need to pick only a few of the many directions surveyed there to dig deeper. It was a game changer for me, nonetheless - it was the book that made me want to work on the field I am now. $\endgroup$ – Pedro Lauridsen Ribeiro Dec 29 '17 at 20:09
  • $\begingroup$ Thanks for the advice. This is what I have been doing but I was wondering if there was some more efficient way to proceed,if such way exist of course. $\endgroup$ – JeffInVermont Dec 31 '17 at 16:19

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