Geodesic
Equivariant $K$-theory of central extensions and twisted equivariant $K$-theory: $SL_{3}\mathbb{Z}$ and $St_{3}{\mathbb{Z}}$
Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 49-70.

Voir la notice de l'article provenant de la source International Press of Boston

We compare twisted equivariant $K$-theory of $SL_{3}{\mathbb{Z}}$ with untwisted equivariant $K$-theory of a central extension $St_3{\mathbb{Z}}$. We compute all twisted equivariant $K$-theory groups of $SL_{3}{\mathbb{Z}}$, and compare them with previous work on the equivariant $K$-theory of $BSt_3{\mathbb{Z}}$ by Tezuka and Yagita. Using a universal coefficient theorem by the authors, the computations explained here give the domain of Baum–Connes assembly maps landing on the topological $K$-theory of twisted group $C^*$-algebras related to $SL_{3}{\mathbb{Z}}$, for which a version of $KK$-theoretic duality studied by Echterhoff, Emerson, and Kim is verified.
DOI : 10.4310/HHA.2016.v18.n1.a4
Classification : 19K33, 19L47, 19L64
Keywords: twisted equivariant $K$-theory, Bredon cohomology, Baum–Connes conjecture with coefficients, twisted group $C^*$-algebra, $KK$-theoretic duality 
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     author = {No\'e B\'arcenas and Mario Vel\'asquez},
     title = {Equivariant $K$-theory of central extensions and twisted equivariant $K$-theory: $SL_{3}\mathbb{Z}$ and $St_{3}{\mathbb{Z}}$},
     journal = {Homology, homotopy, and applications},
     pages = {49--70},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a4/}
}
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Noé Bárcenas; Mario Velásquez. Equivariant $K$-theory of central extensions and twisted equivariant $K$-theory: $SL_{3}\mathbb{Z}$ and $St_{3}{\mathbb{Z}}$. Homology, homotopy, and applications, Tome 18 (2016) no. 1, pp. 49-70. doi : 10.4310/HHA.2016.v18.n1.a4. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2016.v18.n1.a4/

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