Homology of some groups of PL-homeomorphisms of the line
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).
compactly supported piecewise linear homeomorphism of the real line
scientific article; zbMATH DE number 4134331
scientific article