论文标题
无限生物双曲线表面的等轴测组
Isometry groups of infinite-genus hyperbolic surfaces
论文作者
论文摘要
考虑到一个2个策略，要问的一个基本问题是，可以将哪些组实现为歧管上恒定曲率的riemannan指标的等轴测组。在本文中，我们将这些组几乎完整地分类为无限的2个manifolds，没有平面末端。令人惊讶的是，我们表明有一类无数的2个模型类别，每个可计数组都可以作为一个等轴测组（即具有自相似端空间的人）。我们将此结果应用于标准组理论特性的障碍，用于同态形态，差异性和此类2个manifolds的映射类群体。例如，这些群体都不满足山雀的选择。是连贯的；是线性的；可周期性或线性有序；或是剩余的。作为第二个应用程序，我们为映射课程组给出了代数刚度结果。
Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannan metric of constant curvature on the manifold. In this paper, we give a nearly complete classification of such groups for infinite-genus 2-manifolds with no planar ends. Surprisingly, we show there is an uncountable class of such 2-manifolds where every countable group can be realized as an isometry group (namely, those with self-similar end spaces). We apply this result to obtain obstructions to standard group theoretic properties for the groups of homeomorphisms, diffeomorphisms, and the mapping class groups of such 2-manifolds. For example, none of these groups satisfy the Tits Alternative; are coherent; are linear; are cyclically or linearly orderable; or are residually finite. As a second application, we give an algebraic rigidity result for mapping class groups.
