4-manifold topology. I: Subexponential groups
type: Item
instance of: scholarly article
title: 4-manifold topology. I: Subexponential groups
zbMATH Open document ID: 0857.57017
DOI: 10.1007/BF01231454
published in: Inventiones Mathematicae
publication date: 1996-06-18T00:00:00Z
full work available at URL: https://eudml.org/doc/144330
review text: The 4-dimensional surgery and 5-dimensional \(s\)-cobordism theorems are known to be true in the topological category for a certain class of groups called good groups. The class of previously known good groups coincides with the elementary amenable groups [the first author, Proc. Int. Congr. Math., Warszawa 1983, Vol. I, 647-663 (1984; Zbl 0577.57003)], i.e. the class of groups containing all groups of polynomial growth and closed under (1) extension and (2) direct limit. In this fundamental paper, the authors expand the class of known good groups to contain all groups of subexponential growth and those that can be obtained from these by a finite number of application of operations (1) and (2). This is an effective expansion because it is known that elementary amenable groups grow either polynomially or exponentially, and that there are (uncountably many) groups of intermediate growth [\textit{R. I. Grigorchuk}, Math. USSR, Izv. 25, 259-300 (1985); translation from Izv. Akad. Nauk SSSR, Ser. Mat. 48, No. 5, 939-985 (1984; Zbl 0583.20023)], i.e. groups that grow faster than any polynomial but slower than any exponential function.
Mathematics Subject Classification ID: 57N13
Mathematics Subject Classification ID: 57R80
zbMATH DE Number: 871778
zbMATH Keywords: \(s\)-cobordism
zbMATH Keywords: 4-dimensional surgery
zbMATH Keywords: 5-dimensional
zbMATH Keywords: elementary amenable groups
zbMATH Keywords: groups of subexponential growth
author: Michael Freedman
author: Peter Teichner
reviewed by: Alberto Cavicchioli
MaRDI profile type: Publication
cites work: An application of gauge theory to four dimensional topology
cites work: The topology of four-dimensional manifolds
cites work: Q4040346
cites work: DEGREES OF GROWTH OF FINITELY GENERATED GROUPS, AND THE THEORY OF INVARIANT MEANS
cites work: Link groups
cites work: A note on curvature and fundamental group
cites work: Homology and central series of groups
cites work: Q4288980
description: scientific article; zbMATH DE number 871778