论文标题
灵活的Hilbert-Schmidt稳定性与财产（t）组的超线性
Flexible Hilbert-Schmidt stability versus hyperlinearity for property (T) groups
论文作者
论文摘要
我们证明了在柔性HS稳定性的情况下以及更普遍的UCP稳定性的情况下，关于属性（t）组中心扩展的毛延伸的陈述。值得注意的是，该结果应用于表明，如果$ \ text {sp} _ {2g}（\ mathbb z）$灵活地hs stable，则存在一个非HyperlineAr组。此外，证明相同的现象对于在Gromov的密度模型中采样的随机组以及所有无限呈现的性质（T）组一致。这为非杂交组的可能存在提供了新的方向。我们的结果为鲍恩和伯顿的工作产生了Hilbert-schmidt的类似物，与$ \ text {psl} _n（\ Mathbb z）$的灵活的P稳定性有关，以及非sofic群体的存在。
We prove a statement concerning hyperlinearity for central extensions of property (T) groups in the presence of flexible HS-stability, and more generally, weak ucp-stability. Notably, this result is applied to show that if $\text{Sp}_{2g} (\mathbb Z)$ is flexibly HS-stable, then there exists a non-hyperlinear group. Further, the same phenomenon is shown to hold generically for random groups sampled in Gromov's density model, as well as all infinitely presented property (T) groups. This gives new directions for the possible existence of a non-hyperlinear group. Our results yield Hilbert-Schmidt analogues for Bowen and Burton's work relating flexible P-stability of $\text{PSL}_n(\mathbb Z)$ and the existence of non-sofic groups.
