具有预定第二$\ell^2$-Betti数的16维Kazhdan群
群论
2026-05-11 v2
摘要
我们构造了一族具有财产(T)且有理编织维数为16的简单、稀疏的双曲群，其第二-Betti数可预定为任意正实数。此外，我们构造了具有财产(T)的双曲群，其第二-Betti数可预定为任意非负有理数。沿途，我们提出了可测多样性有限生成群的新建构方法，并证明第二-Betti数在标志群空间中远非半连续，即使在假设良好有限性质的前提下也是如此。
引用
@article{arxiv.2601.00074,
title = {Kazhdan groups of dimension $16$ with prescribed second $\ell^2$-Betti number},
author = {Francesco Fournier-Facio and Roman Sauer},
journal= {arXiv preprint arXiv:2601.00074},
year = {2026}
}
备注
25 pages. v2: improved, now the second l2-Betti numbers of the groups in Theorem A are not just in an uncountable range, but can be any positive real (hence the change in the title). Moreover the new Theorem B constructs hyperbolic groups with prescribed rational second l2-Betti number