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Can anyone give me some good references to read geometric K-homology. I know bit of Kasparov's KK theory and analytic K-homology.

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up vote 5 down vote accepted

If I remenber correctly one can use, Martin Jakob's geometric approach to generalized homology theories:

Jakob, Martin An alternative approach to homology. Une dégustation topologique [Topological morsels]: homotopy theory in the Swiss Alps (Arolla, 1999), 87–97, Contemp. Math., 265, Amer. Math. Soc., Providence, RI, 2000.

Jakob, Martin A bordism-type description of homology. Manuscripta Math. 96 (1998), no. 1, 67–80.

Baum-Douglas geometric K-homology groups are defined in this way, this is very well explained in (sections 4 and 5 in the arXiv version):

Baum, Paul; Higson, Nigel; Schick, Thomas On the equivalence of geometric and analytic $K$-homology. Pure Appl. Math. Q. 3 (2007), no. 1, part 3, 1–24.

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