4-MANIFOLD TOPOLOGY .1. SUBEXPONENTIAL GROUPS
成果类型：
Article
署名作者：
FREEDMAN, MH; TEICHNER, P
署名单位：
Johannes Gutenberg University of Mainz
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/BF01231454
发表日期：
1995
页码：
509-529
关键词：
摘要：
The technical lemma underlying the 5-dimensional topological s-cobordism conjecture and the 4-dimensional topological surgery conjecture is a purely smooth category statement about locating pi(1)-null immersions of disks. These conjectures are theorems precisely for those fundamental groups (''good groups'') where the pi(1)-null disk lemma (NDL) holds. We expand the class of known good groups to all groups of subexponential growth and those that can be formed from these by a finite number of application of two operations: (1) extension and (2) direct limit. The finitely generated groups in this class are amenable and no amenable group is known to lie outside this class.