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I have recently decided on a topic for my master thesis. I want to compare the Baum Connes conjecture as it is formulated in topology to the conjecture as it is formulated in functional analysis. I understand that everybody assumes that they are basically the same, but nobody has put in the work to actually show it - that is my job now. For the analytical point of view I checked the introductory book by Valette, and for the topological point of view an article by Lueck and Reich. Now I am a bit overwhelmed by the mass of information that has come my way - I don't actually see much of a difference to be honest. What I would like is a few recommendations what books to read and maybe where to find a clear cut difference.

Thank you.

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    $\begingroup$ do you have an advisor for this thesis project? it is unlikely that MO can take the place of an academic advisor. $\endgroup$
    – Carlo Beenakker
    Commented Jul 10, 2016 at 10:00
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    $\begingroup$ The BC conjecture is not "formulated in topology" or "formulated in functional analysis", it's always formulated in both, as it asserts that two objects from topology and functional analysis are isomorphic (and the prerequisites usually construct the assembly map, conjectured to be a bijection). $\endgroup$
    – YCor
    Commented Jul 10, 2016 at 10:33
  • $\begingroup$ Thank you for your replies. I actually have two advisors, one works in topology and one works in functonal analysis. I know that it is always fomrulated in both, but apparently the way to look at the left side of the conjecture is different. $\endgroup$
    – Hodor
    Commented Jul 10, 2016 at 10:48
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    $\begingroup$ Anyway, I don't have any idea what you are asking. To make a difference between what? between topology and functional analysis? Valette's book is a basic introduction to the subject, with little prerequisite, the best is probably to work with it (if you are already overwhelmed by the mass of information that came your way, isn't it contradictory to ask for more books?). $\endgroup$
    – YCor
    Commented Jul 10, 2016 at 13:09
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    $\begingroup$ I also agree strongly with @CarloBeenakker's comment. MO should be consulted after talking to your local advisors, not instead of them. $\endgroup$
    – Yemon Choi
    Commented Jul 10, 2016 at 16:32

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