Homology of some groups of PL-homeomorphisms of the line
type: Item
instance of: scholarly article
title: Homology of some groups of PL-homeomorphisms of the line
zbMATH Open document ID: 0693.20047
DOI: 10.1016/0166-8641(89)90108-9
author: Peter Greenberg
published in: Topology and its Applications
publication date: 1989-01-01T00:00:00Z
review text: A description of the homology of a family \(\{K^ n\); \(n\geq 1\}\) of groups of compactly supported piecewise linear homeomorphism of the real line \({\mathbb{R}}\) having suitable additional properties defined in terms of breakpoints (points of discontinuity of the derivative) is given in terms of classifying spaces of suitable pseudogroups on the real line and related spaces. The additional properties characterizing the groups \(K^ n\) are too complicated to be spelled out here; a special case would be the requirement that the breakpoints are isolated. In particular, it turns out that, for \(n\geq 1\), the homology \(H_*(K^ n)\) vanishes whenever \(0<*<n\) and that the obvious map \(K^ n\to K^{n+1}\) induces the zero map on homology. The latter results rely on various results involving pseudogroups on the real line, which are given in (1.4) and (1.11).
reviewed by: J. Huebschmann
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 58H05
Mathematics Subject Classification ID: 58H10
zbMATH DE Number: 4134331
zbMATH Keywords: homology
zbMATH Keywords: compactly supported piecewise linear homeomorphism of the real line
zbMATH Keywords: classifying spaces
zbMATH Keywords: pseudogroups
MaRDI profile type: Publication
full work available at URL: 0166-8641(89)90108-9
OpenAlex ID: W2045198741
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description: scientific article; zbMATH DE number 4134331