图上的紧树与曲面丛的模型几何
Tight trees and model geometries of surface bundles over graphs
摘要：
我们推广的概念紧测地线的曲线复杂的紧树。然后，我们使用紧树构建模型几何图形的某些表面束。这扩展了布罗克、金丝雀和明斯基在证明终结层合定理的过程中所建立的双退化双曲三维流形的组合模型的某些方面。这样我们得到了具有几何$G-$作用的一致Gromov-双曲几何模型空间，其中$G$允许$$1 \to π_1(S) \to G \to Q \to 1.$$形式的正合序列这里$S$是亏格$g > 1$的闭曲面，$Q$属于映射类群$MCG(S)$的一类特殊的自由凸余紧子群.
英文摘要：
We generalize the notion of tight geodesics in the curve complex to tight trees. We then use tight trees to construct model geometries for certain surface bundles over graphs. This extends some aspects of the combinatorial model for doubly degenerate hyperbolic 3-manifolds developed by Brock, Canary, and Minsky during the course of their proof of the Ending Lamination Theorem. Thus we obtain uniformly Gromov-hyperbolic geometric model spaces equipped with geometric $G-$actions, where $G$ admits an exact sequence of the form $$1 \to π_1(S) \to G \to Q \to 1.$$ Here $S$ is a closed surface of genus $g > 1$ and $Q$ belongs to a special class of free convex cocompact subgroups of the mapping class group $MCG(S)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
