论文标题
更高的kazhdan预测，$ \ ell_2 $ -betti号码和鲍姆 - 康纳斯猜想
Higher Kazhdan projections, $\ell_2$-Betti numbers and Baum-Connes conjectures
论文作者
论文摘要
我们在$ C^*$ - 代数 - 代数和ROE代数上引入了矩阵代数的Kazhdan预测的高维类似物。这些预测是在共同体的框架内建立的，其系数在单一表示中，在某些情况下会产生非平凡的$ K $理论类。我们应用较高的Kazhdan预测，以建立$ \ ell_2 $ -betti组数量和不同Baum-Connes类型装配图的溢流性之间的关系。
We introduce higher-dimensional analogs of Kazhdan projections in matrix algebras over group $C^*$-algebras and Roe algebras. These projections are constructed in the framework of cohomology with coefficients in unitary representations and in certain cases give rise to non-trivial $K$-theory classes. We apply the higher Kazhdan projections to establish a relation between $\ell_2$-Betti numbers of a group and surjectivity of different Baum-Connes type assembly maps.
