تقرير
K-theory and K-homology of the wreath products of finite with free groups
| العنوان: | K-theory and K-homology of the wreath products of finite with free groups |
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| المؤلفون: | Pooya, Sanaz |
| المصدر: | Illinois J. Math. 63, no. 2 (2019), 317-334 |
| سنة النشر: | 2017 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Operator Algebras, Mathematics - Algebraic Topology, Mathematics - Group Theory, Mathematics - K-Theory and Homology |
| الوصف: | Consider the wreath product $\Gamma = F\wr \mathrm{F_n} = \bigoplus_{\mathrm{F_n}}F\rtimes\mathrm{F_n}$, with $F$ a finite group and $\mathrm{F_n}$ the free group on $n$ generators. We study the Baum-Connes conjecture for this group. Our aim is to explicitly describe the Baum-Connes assembly map for $F\wr \mathrm{F_n}$. To this end, we compute the topological and the analytical K-groups and exhibit their generators. Moreover, we present a concrete 2-dimensional model for $\underline{E} \Gamma$. As a result of our K-theoretic computations, we obtain that $\mathrm K_0(\mathrm C^*_{\mathrm r}(\Gamma))$ is the free abelian group of countable rank with a basis consisting of projections in $\mathrm C^*_{\mathrm r}(\bigoplus_{\mathrm{F_n}}F)$ and $\mathrm K_1(\mathrm C^*_{\mathrm r}(\Gamma))$ is the free abelian group of rank $n$ with a basis consisting of the unitaries coming from the free group. Comment: 18 pages |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1215/00192082-7768735 |
| URL الوصول: | http://arxiv.org/abs/1707.05984 |
| رقم الأكسشن: | edsarx.1707.05984 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1215/00192082-7768735 |
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