Mathematical Sciences: Topology

这个项目涵盖了代数和几何拓扑学的广泛主题。更具体地说，研究人员研究了各种离散群的组合和几何性质，包括有限表示的无限单群、重写系统表示的群、群的三角形表示的群以及自由或有限自由群的自同构群：(B)三维流形中的叠片；(C)等变拓扑和受控拓扑，包括局部可线性化作用的等变拓扑和线性表示的拓扑等价。拓扑学处理与距离或角度无关的几何属性。然而，它试图找到比较拓扑对象的方法，并在许多情况下将它们的研究归结为计算。即时项目参与了这项繁杂工作的不同方面。

This project covers a wide range of topics in algebraic and geometric topology. More specifically, the researchers study the following: (a) Combinatorial and geometric properties of various classes of discrete groups, including finitely presented infinite simple groups, groups presented by a rewriting system, groups presented by a triangle of groups, and the automorphism group of a free or free-by-finite group; (b) laminations in 3-manifolds; (c) equivariant and controlled topology, including the equivariant topology of locally linearizable actions and the topological equivalence of linear representations. Topology addresses geometric properties which do not depend in an essential way on distances or angles. It nevertheless attempts to find ways to compare topological objects and to reduce their study to computations in many cases. The instant project is engaged in different aspects of this multifarious effort.