Instead, this is me bemoaning one thing that has bugged me on and off when trying to learn more about certain topics – and by learning, I don’t mean in the leisurely sense of broadening one’s mathematical background, but rather as a necessary precursor to finding and exploring avenues of research.
So: to those who make use in textbooks or survey articles or even their own research articles of big results “due to Connes” or “due to Dixmier” – could one of you at least take the time to untangle how the proofs actually work? Not in detail, but just to point out that statements along the lines of
the von Neumann algebra of an almost connected group is Connes-amenable, and this is due to Connes in his Annals paper classifying injective factors
are actually misleading? One might get the impression that people cite these things without looking at the original papers to see where the proof is given… (Hint: if Pukanszky doesn’t get mentioned, then the account is either inadvertently or willfully cutting corners.)
May expand on this particular peeve of mine – and a more general bugbear of mine, that the incentives in mathematics have drifted away from understanding and refining what we’ve proved, to shouty advertising and Toiling At The Coalface – if I can get my own notes organised. So probably not, then…
Edited 21-12-09: On rereading this bit of grumbling, I see that I may have given a misleading impression, or at least sinned against some W3C specification, with that “blockquote” above. It isn’t a genuine quote from anything, but rather my own version of what several sources have seemed to imply. Moreover, the result claimed is both true and non-trivial — but I think I’ll save further discussion for a separate post.