JS']JSJ-splittings for finitely presented groups over slender groups

被引：64

作者：

Dunwoody, MJ ^{[1
]}

Sageev, ME

机构：

[1] Univ Southampton, Fac Math Studies, Southampton SO17 1BJ, Hants, England

[2] Rutgers State Univ, Dept Math & Comp Sci, Newark, NJ 07102 USA

来源：

INVENTIONES MATHEMATICAE | 1999年 / 135卷 / 01期

关键词：

Small Subgroup; Ambient Group; Slender Group;

D O I：

10.1007/s002220050278

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We generalize the JSJ-splitting of Rips and Sela to give decompositions of finitely presented groups which capture splittings over certain classes of small subgroups. Such classes include the class of all 2-ended groups and the class of all virtually Z + Z groups. The approach, called "track zipping", is relatively elementary, and differs from the Rips-Sela approach in that it does not rely on the theory of R-trees but rather on an understanding of certain embedded 1-complexes (called patterns) in a presentation 2-complex for the ambient group.

引用

页码：25 / 44

页数：20