论文标题
复杂双曲线晶格的最大可测量共生的超级汇率
Superrigidity of maximal measurable cocycles of complex hyperbolic lattices
论文作者
论文摘要
令$γ$为$ \ text {pu}（p，1）$的无扭转晶格，带$ p \ geq 2 $，让$（x，μ_x）$为ergodic标准borel borel概率$γ$ - 空间。我们证明，任何最大的Zariski致密共生$σ：γ\ times x \ longrightArrow \ text {su}（m，n）$都是与$ \ text {pu}（p，p，1）$ to $ \ tox $ \ text $ \ text cocyclapations cocycle cosomology copology cocymology cocymology证明遵循Zimmer's Superrigity定理的线，需要一个边界图的存在，我们在更一般的环境中证明了边界图。由于我们的结果，当$ n \ neq m $ $时，它不能与上述属性具有最大可测量的共同体。
Let $Γ$ be a torsion-free lattice of $\text{PU}(p,1)$ with $p \geq 2$ and let $(X,μ_X)$ be an ergodic standard Borel probability $Γ$-space. We prove that any maximal Zariski dense measurable cocycle $σ: Γ\times X \longrightarrow \text{SU}(m,n)$ is cohomologous to a cocycle associated to a representation of $\text{PU}(p,1)$ into $\text{SU}(m,n)$, with $1 < m \leq n$. The proof follows the line of Zimmer' Superrigidity Theorem and requires the existence of a boundary map, that we prove in a much more general setting. As a consequence of our result, it cannot exist a maximal measurable cocycle with the above properties when $n\neq m$.
