单关系群的高阶Kazhdan投影
Higher Kazhdan projections for one relator groups
- University of Potsdam（波茨坦大学）
- East China Normal University（华东师范大学）
- Universität Göttingen（哥廷根大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
该研究针对第一拉普拉斯算子具谱间隙的有限生成无限单关系群，给出第一高阶Kazhdan投影的K-理论类的显式描述，还为双曲单关系群提供非局部化ℓ²-Betti数的对应公式。
中文摘要 AI 辅助
我们研究离散群在谱间隙假设下的高阶Kazhdan投影的K-理论类，并回顾它们如何通过Baum–Connes装配映射从等变欧拉类得到。在回顾了virtually free群的情况（其真作用的通用空间有一维模型）后，我们证明了主要新结果：对于第一拉普拉斯算子具有谱间隙的有限生成无限单关系群，第一高阶Kazhdan投影的K-理论类的显式描述。此外，若该单关系群是双曲的，这也给出了非局部化ℓ²-Betti数的对应公式。
英文摘要
We study the $K$-theory classes of higher Kazhdan projections of a discrete group under a spectral-gap assumption and recall how they are obtained, via the Baum--Connes assembly map, from equivariant Euler classes. After reviewing the case of virtually free groups, where the universal space for proper actions has a one-dimensional model, we prove the main new result: an explicit description of the $K$-theory class of the first higher Kazhdan projection for finitely generated infinite one-relator groups whose first Laplacian has a spectral gap. If moreover the one-relator group is hyperbolic, this also gives corresponding formulas for delocalised $\ell^2$-Betti numbers.
