论文标题
在拓扑上的大轨迹上
On Topologically Big Divergent Trajectories
论文作者
论文摘要
我们研究$ g/γ$的$ a $ orbits的行为时，当$ g $是一个半胶合实际代数$ \ mathbb {q} $ - 组，$γ$是一个不均匀的算术质量质量，而$ $ a $是dimension $ \ geq \ geq \ epropornAmeAneame {n等级$ a $ a $ a $我们表明，由于纯粹的代数原因，每一个$ a $ a $ a差异的轨迹都具有简单的代数描述。解决了魏斯的长期猜想。此外，我们检查了$ a-orbits的交叉点，并表明在许多情况下，每$ a $ a $ orbit都会相交每个变形缩回$ x \ subseteq g/γ$。这解决了Pettet和Souto提出的问题。这些证明使用代数和差异拓扑以及代数群体理论。
We study the behavior of $A$-orbits in $G/Γ$, when $G$ is a semisimple real algebraic $\mathbb{Q}$-group, $Γ$ is a non-uniform arithmetic lattice, and $A$ is a torus of dimension $\geq\operatorname{rank}_\mathbb{Q}(Γ)$. We show that every divergent trajectory of $A$ diverges due to a purely algebraic reason, % has a simple algebraic description. solving a longlasting conjecture of Weiss. In addition, we examine the intersections of $A$-orbits and show that in many cases every $A$-orbit intersects every deformation retract $X\subseteq G/Γ$. This solves the questions raised by Pettet and Souto. The proofs use algebraic and differential topology, as well as algebraic group theory.
