论文标题
边界图和合子的降低性到CAT（0）空间的异构体
Boundary maps and reducibility for cocycles into the isometries of CAT(0)-spaces
论文作者
论文摘要
令$γ$成为一个可离散的可计数组，在某些Ergodic标准Borel概率$γ$ -Space $（ω，μ）$上，在有限望远镜尺寸的CAT（0）cat（0） - cat（0） - cat（0） - cat（0） - 空格的可测量群体上作用。如果$ \ mathbf {x} $不承认任何不变的欧几里得子场，我们证明可测量的字段$ \ wideHat {\ mathbf {x}} $扩展到$γ$ buge-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-B-Bivention consens cons n varariant consens。在恒定场的情况下，这表明存在可测量的共体的Furstenberg地图，从而扩大了Bader，Duchesne和Lécureux的结果。 当$γ<\ mathrm {pu}（n，1）$是无扭转的晶格，而cat（0） - 空间为$ \ nathcal {x}}（p，p，\ infty）$时，我们表明，最大cocycle $之一可还原。结果，我们证明了$ \ mathrm {pu}（1，\ infty）$中最大旋转的无限尺寸刚度现象。
Let $Γ$ be a discrete countable group acting isometrically on a measurable field $\mathbf{X}$ of CAT(0)-spaces of finite telescopic dimension over some ergodic standard Borel probability $Γ$-space $(Ω,μ)$. If $\mathbf{X}$ does not admit any invariant Euclidean subfield, we prove that the measurable field $\widehat{\mathbf{X}}$ extended to a $Γ$-boundary admits an invariant section. In the case of constant fields this shows the existence of Furstenberg maps for measurable cocycles, extending results by Bader, Duchesne and Lécureux. When $Γ<\mathrm{PU}(n,1)$ is a torsion-free lattice and the CAT(0)-space is $\mathcal{X}(p,\infty)$, we show that a maximal cocycle $σ:Γ\times Ω\rightarrow \mathrm{PU}(p,\infty)$ with a suitable boundary map is finitely reducible. As a consequence, we prove an infinite dimensional rigidity phenomenon for maximal cocycles in $\mathrm{PU}(1,\infty)$.
