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Question: What is the motivation for cyclic (co)homology?

Comment: There are two types of things which can motivate such notion. Natural construction in which they appear (for example Hochschild cohomology have natural description in means of classical homological algebra). Or at least lemmas that they compute something sensible (like second Hochschild cohomology are deformations of algebra). I am looking for both kinds of motivation.

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    $\begingroup$ See page 19 of alainconnes.org/docs/book94bigpdf.pdf $\endgroup$
    – Jon Bannon
    Commented Jan 17, 2015 at 12:04
  • $\begingroup$ Is there some application which are more elementary than connection with algebraic K-theory? $\endgroup$
    – quinque
    Commented Jan 17, 2015 at 12:51
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    $\begingroup$ Might this people.math.osu.edu/ramsey.313/papers/CyclicSurvey.pdf be the kind of thing you are looking for? It might help if you explained what you are looking for in terms of "more elementary" applications $\endgroup$
    – Yemon Choi
    Commented Jan 17, 2015 at 13:38
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    $\begingroup$ Regarding the recent retagging: the KT tag serves useful taxonomy: it doesn't really seem worth adding homology or cohomology tags since the question really is about cyclic (co)homology, not group cohomology or singular homology etc etc etc $\endgroup$
    – Yemon Choi
    Commented Jul 1, 2019 at 4:29

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