标题： 更高Kazhdan投影和粘合积群的非局部化$\ell^2$-Betti数 显示英文标题

标题： Higher Kazhdan projections and delocalized $\ell^2$-Betti numbers for an amalgamated product group

摘要： 我们建立了更高Kazhdan投影的并积群$\mathbb{Z}_m*_{\mathbb{Z}_d}\mathbb{Z}_n$的$K$理论类的显式表达式。 我们的方法遵循Pooya和Wang对自由积群$\mathbb{Z}_m*\mathbb{Z}_n$开发的方法，并自然地推广了他们在自由积上的结果。 作为$K$类表达式的应用，我们得到了并积群$\mathrm{SL}(2,\mathbb{Z})$的非退化$\ell^2$贝蒂数的非零结果。 显示英文摘要

摘要： We establish explicit expressions for the $K$-theory classes of higher Kazhdan projections for amalgamated product groups $\mathbb{Z}_m*_{\mathbb{Z}_d}\mathbb{Z}_n$. Our approach follows the methodology developed by Pooya and Wang for free product groups $\mathbb{Z}_m*\mathbb{Z}_n$, and naturally generalizes their results on free products. As an application of the $K$-class expressions, we obtain non-vanishing results for delocalized $\ell^2$-Betti numbers of $\mathrm{SL}(2,\mathbb{Z})$.