Mapping the homology of a group to the $K$-theory of its $C\sp *$-algebra
Matthey, Michel
Illinois J. Math., Tome 46 (2002) no. 3, p. 953-977 / Harvested from Project Euclid
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For a CW-complex $X$ and for $0\leq j\leq 2$, we construct natural homomorphisms $\beta_{j}^{X}\colon H_{j}(X;\,\mathbb{Z}) \longrightarrow K_{j}(X)$ that are rationally right-inverses of the Chern character. We show that $\beta_{j}^{X}$ is injective for $j=0$ and $j=1$. The case $j=3$ is treated using $\mathbb{Z}[\frac12]$-coefficients. The study of these maps is motivated by the connection with the Baum-Connes conjecture on the $K$-theory of group $C^{*}$-algebras.
Publié le : 2002-07-15
Classification:  19K56,  19L10,  19L41,  55S45,  57R20 
@article{1258130995,
     author = {Matthey, Michel},
     title = {Mapping the homology of a group to the $K$-theory of its $C\sp *$-algebra},
     journal = {Illinois J. Math.},
     volume = {46},
     number = {3},
     year = {2002},
     pages = { 953-977},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258130995}
}

Matthey, Michel. Mapping the homology of a group to the $K$-theory of its $C\sp *$-algebra. Illinois J. Math., Tome 46 (2002) no. 3, pp.  953-977. http://gdmltest.u-ga.fr/item/1258130995/