A refinement of the simple connectivity at infinity of groups

闭合曲面的映射类群在无穷处的更高连通性

The higher connectivity at infinity of mapping class groups

本文证明了闭合曲面的映射类群在无穷处单连通，并给出了其连通性的完整列表。

双曲群与局部连通性

Hyperbolic groups and local connectivity

本文阐述 Bestvina-Mess 关于单端字双曲群边界局部连通性的结果，并用初等方法证明双曲群在无穷远处半稳定且单端情形下边界线性连通。

Connectivity at Infinity for the Braid Group of a Complete Bipartite Graph

The graph braid group of a complete bipartite graph is the fundamental group of a configuration space of points on the graph, which is a CAT(0) cube complex. We combine an analysis of the topology of links of vertices in this complex, the description of a hidden symmetry among the parameters, and known results from the literature to explicitly compute the exact degree to which these complexes and groups are connected at infinity.

Connectivity properties of group actions on non-positively curved spaces II: The geometric invariants

This is the second of two papers but has been written so as to have minimal dependence on the first paper (which is also on this archive). Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Assume G is of type F_n (type F_1 is finitely generated, type F_2 is finitely presented etc.) The "boundary", bdM, of M at infinity has two customary topologies - the compact "cone" topology and the Tits metric topology. We associate with any isometric action of G on M two subsets of …

Topics in Geometric Group Theory. Part I

This survey paper concerns mainly with some asymptotic topological properties of finitely presented discrete groups: quasi-simple filtration (QSF), geometric simple connectivity (GSC), topological inverse-representations, and the notion of easy groups. As we will explain, these properties are central in the theory of discrete groups seen from a topological viewpoint at infinity. Also, we shall outline the main steps of the achievements obtained in the last years around the very general question whether or not all finitely presented groups satisfy these conditions.