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nLab > Latest Changes: K-homology

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    • CommentRowNumber1.
    • CommentAuthorDmitri Pavlov
    • CommentTimeJul 26th 2023

    Added:

    An expository account of the analytic model:

    • N. Higson, J. Roe, Analytic K-homology, Oxford Mathematical Monographs. Oxford University Press, Oxford, 2000, Oxford Science Publications. ISBN: 9780198511762

    diff, v8, current

    • CommentRowNumber2.
    • CommentAuthorzskoda
    • CommentTimeJul 26th 2023

    Is “analytic model” have a technical meaning ? Model of what ?

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2023

    K-(co)homology groups have an abstract definition and a variety of concrete presentations by auxiliary data. The “analytic model” for K-homology is a presentation of the K-homology groups by operator algebra/analysis, in contrast to the “geometric model” by Baum & Douglas, which constructs the same groups but along a different route.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJul 26th 2023

    added the original references for the “geometric model” of K-homology (cf. Baum-Douglas geometric cycle):

    • Paul Baum, R. Douglas, K-homology and index theory, in: R. Kadison (ed.), *Operator Algebras and Applications, Proceedings of Symposia in Pure Math. 38 AMS (1982) 117-173 [ams:pspum-38-1]

    • Paul Baum, R. Douglas. Index theory, bordism, and K-homology, Contemp. Math. 10 (1982) 1-31

    diff, v9, current

1 to 4 of 4

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