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I've been looking at KK-theory related subjects for some time now with both the Cuntz (quasihomomorphism) and Kasparov (Fredholm) picture. However, recently i've found myself needing the Ext picture.

KK-theory seems slightly difficult to look for in the literature if you avoid Kasparov's original papers. I was wondering if anyone knows a good reference for

  • KK-theory and some of the proofs for existence of the Kasparov product.
  • The Ext-picture of KK-theory and why they are isomorphic.

I currently hold Blackadar's book on K-theory, but I find myself proving most of the things and i'd like to sanity check as well.

Thanks in advance!

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I can recommend the book "Elements of KK-theory" by Jensen and Thomsen if you want to fill in the details that Blackadar skips. Not a lot of examples in this book though, but it contains a lot of details!

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