Asymptotically CAT(0) Groups

Journal article

We study the general theory of asymptotically CAT(0) groups, explaining why such a group has finitely many conjugacy classes of finite subgroups, is $F_\infty$ and has solvable word problem. We provide techniques to combine asymptotically CAT(0) groups via direct products, amalgams and HNN extensions. The universal cover of the Lie group $PSL(2,\mathbb{R})$ is shown to be an asymptotically CAT(0) metric space. Therefore, co-compact lattices in $\widetilde{PSL(2,\mathbb{R})}$ provide the first examples of asymptotically CAT(0) groups which are neither CAT(0) nor hyperbolic. Another source of examples is shown to be the class of relatively hyperbolic groups.

Authors: Kar, A

• Publication status: Published
• Journal: PUBLICACIONS MATEMATIQUES
• Volume: 55
• Issue: 1
• Pages: 67-91
• Publication date: 2008-10-22
• DOI: 10.5565/PUBLMAT_55111_04
• ISSN: 0214-1493
• Language: English
• Keywords: 20F65; math.GR