论文标题
自由群体的拓扑，几何和动力学。第一部分：外层空间，折叠路径和尼尔森/怀特黑德问题
The topology, geometry and dynamics of free groups. Part I: Outer space, fold paths, and the Nielsen/Whitehead problems
论文作者
论文摘要
这项说明性工作的目的是试图揭示自由群体及其自动形态和外部自动形态群体背后的拓扑/几何直觉。我们遵循的方法是专注于自由组研究中的一系列问题，并使用这些问题的解决方案来激发拓扑/几何工具。我们的目的不是写下最小化字母数字数量的证据。相反，我们努力写下证据，以最大限度地开发广泛适用的几何工具。 在第一部分中，我们研究了Nielsen和Whitehead在1920年代和1930年代解决的问题，但是我们从现代的拓扑/几何学角度来解决这些问题，我们制定了它们的解决方案，以激发现代工具，包括标记的图形，自由组的外层空间，以及外在空间中的折叠路径。
The object of this expository work is to try to unveil the topological/geometric intuition behind the theory of free groups and their automorphism and outer automorphism groups. The method we follow is to focus on a series of problems in the study of free groups, and use the solutions of those problems to motivate topological/geometric tools. We do not aim to write down proofs which minimize the number of alphanumeric characters. We instead strive to write down proofs which maximize the development of broadly applicable geometric tools. In Part I we study problems solved by Nielsen and Whitehead in the 1920's and 1930's, but we approach these problems from a modern topological/geometric viewpoint, and we formulate their solutions so as to motivate modern tools, including marked graphs, the outer space of a free group, and fold paths in outer space.
