Geometry of Groups and Splittings

群和分裂的几何这个项目有四个组成部分。第一个部分需要研究群的高维填充不变量，重点是构造展示所有可能行为的例子。Forester及其合作者Brady、Bridson和Shankar打算开发计算此类不变量的一般方法，并研究子群扭曲和曲率的作用。第二部分是关于特殊类群的几何结构的构造，例如极限群，以及这些群的子群和末端的结构的研究。在第三个组成部分中，Forester将研究广义Baumlash-Solitar群的分类并进行应用。在第四部分中，Forester将继续他与Rourke在多变量伴随问题上的工作，在无挠群的情况下。这项工作是对Klyachko方法的推广和发展。群论是对称论，它在数学中起着基础性的作用。对称性(或“群”)的概念非常自然地出现在几何学中，但也出现在其他更抽象的领域。在几何群论领域，人们通过构造几何空间来研究抽象群，这些几何空间是为手边的群量身定做的，以便“看到”对称性并理解它。这个项目涉及到对所构造的几何空间的详细研究。

Geometry of Groups and SplittingsThis project has four components. The first component entails the studyof higher dimensional filling invariants of groups, with emphasis oncontructing examples exhibiting the full range of possiblebehavior. Forester and collaborators Brady, Bridson, and Shankar intendto develop general methods for computing such invariants, and to studythe role of subgroup distortion and curvature. The second componentconcerns the construction of geometric structures for particular classesof groups, such as limit groups, and the study of the structure ofsubgroups and ends for these groups. In the third component Forester willinvestigate the classification of generalized Baumslag-Solitar groupsand pursue applications. In the fourth component Forester will continuehis work with Rourke on the multivariable adjunction problem, in the caseof torsion-free groups. This work extends and devolops Klyachko'smethods.Group theory is the theory of symmetry, which plays a fundamental role inmathematics. Notions of symmetry (or "groups") arise very naturally ingeometry, but also in other, more abstract, areas. In the field ofgeometric group theory one studies abstract groups by constructinggeometric spaces, tailor-made for the groups at hand, in order to "see"the symmetry and understand it. This project involves the detailed studyof the geometric spaces thus constructed.