Mathematical Sciences: Topology

这个项目涵盖了广泛的主题，在代数和 几何拓扑学 更具体地说，研究人员研究了 （a）各种不同的组合和几何性质 离散群的类，包括不存在的无限群 简单群，重写系统表示的群，群 一个三角形的群，和自同构群， （B）3-流形中的叠层; (c)等变和受控拓扑，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 拓扑处理不依赖于 in an essential本质way on distance距离or angles角度. 它仍然 试图找到比较拓扑对象的方法， 在许多情况下，他们把研究简化为计算。 本 该项目是从事这个多方面的不同方面， 努力

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.