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 there 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 recommendation what books to read and maybe where to find a clear cut difference.

Thank you.