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There exist unpublished notes on correspondences of von Neumann algebras due to Connes. This is often cited, but I've never seen a copy. It would be nice to have this, say, to maybe look further into the point of view discussed in his book Noncommutative geometry. Particularly, the stuff involving half-densities.

Does anyone have a scanned copy of this they wouldn't mind sending/posting a link to?

Thanks, in advance!

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Aren't you thinking of Popa's unpublished manuscript on Correspondences, available on his website: http://www.math.ucla.edu/~popa/popa-correspondences.pdf

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  • $\begingroup$ Thanks, Alain! I do, in fact, mean unpublished notes of Connes, though. I wonder if Sorin Popa would have a copy of these? $\endgroup$
    – Jon Bannon
    Commented Apr 29, 2011 at 11:30
  • $\begingroup$ I see. These might be handwritten notes by Connes, dated 1980, right? I don't have them. Most probably Sorin has a copy, or Dima, or Claire Anantharaman-Delaroche... $\endgroup$
    – Alain Valette
    Commented Apr 29, 2011 at 12:01
  • $\begingroup$ Yes, these are the notes I'm referring to. $\endgroup$
    – Jon Bannon
    Commented Apr 29, 2011 at 12:24
  • $\begingroup$ I wonder if these notes more or less are contained in Connes's book? I have never seen the notes, so I don't know. $\endgroup$
    – Jon Bannon
    Commented Apr 29, 2011 at 12:25
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    $\begingroup$ Hi @JonBannon :) Looking in the draft book of CAD & Popa, they say at one point: "the notion of bimodule was introduced by Connes in the beginning of the eighties...The content of his unpublished manuscript notes that were circulated at that time may be found in his book [Con94, V. Appendix B] where bimodules are called correspondences." Perhaps you already saw the stuff in his book? $\endgroup$
    – Yemon Choi
    Commented Feb 12, 2019 at 18:16

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