论文标题
具有负弯曲的歧管的有界共同体中的杯子产品
Cup product in bounded cohomology of negatively curved manifolds
论文作者
论文摘要
令$ m $成为带有（可能为空的）凸边界的负弯曲的紧凑型riemannian歧管。每个关闭的差异$ 2 $ -form $ξ\inΩ^2（m）$通过集成$ 2 $ 2 $ -simplices来定义c_b^2（m）$中的有界的cocycle $c_ξ\。尤其是驳船和盖斯证明，当$ m $是封闭的双曲线表面时，$ω^2（m）$以$ h_b^2（m）$作为无限维度子空间注入。我们表明，$ [C_ξ] $的任何类别的$ [c_ξ] $，其中$ξ$是确切的微分2形，属于分级代数$ h_b^\ bullet（m）$的杯产物的根本。
Let $M$ be a negatively curved compact Riemannian manifold with (possibly empty) convex boundary. Every closed differential $2$-form $ξ\inΩ^2(M)$ defines a bounded cocycle $c_ξ\in C_b^2(M)$ by integrating $ξ$ over straightened $2$-simplices. In particular Barge and Ghys proved that, when $M$ is a closed hyperbolic surface, $Ω^2(M)$ injects this way in $H_b^2(M)$ as an infinite dimensional subspace. We show that any class of the form $[c_ξ]$, where $ξ$ is an exact differential 2-form, belongs to the radical of the cup product on the graded algebra $H_b^\bullet(M)$.
