Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration finite foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).

nLab > Latest Changes: K-homology

Bottom of Page

1 to 4 of 4

  1.  
    • 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

  1.