Grabowski, Janusz Free subgroups of diffeomorphism groups. (English) Zbl 0666.58011 Fundam. Math. 131, No. 2, 103-121 (1988). It is well known that, for all \(k\in \{1,2,...,\infty \}\), the group \(Diff^ k_ c(X)\) of all compactly supported \(C^ k\)-diffeomorphisms of the \(C^ k\)-manifold X contains elements arbitrarily close to the identity which belong to no 1-parameter subgroup. In this paper, the author strengthens this result, showing that \(Diff^ k_ c(X)\) in fact contains an arc-connected subgroup consisting of such elements. Moreover, one can assume this subgroup is freely generated by the elements \(\gamma\) (t), \(t\in (0,1)\), where \(\gamma\) : [0,1)\(\to Diff^ k_ c(X)\) is a continuous map with \(\gamma (0)=id.\) As an intermediate step in the proof, the author shows that, given any sequence of elements in \(Diff^ k_ c(X)\), there are diffeomorphisms arbitrarily close to the given ones which are free generators of a subgroup in \(Diff^ k_ c(X)\). Reviewer: D.McDuff Cited in 20 Documents MSC: 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds 57R50 Differential topological aspects of diffeomorphisms 58B25 Group structures and generalizations on infinite-dimensional manifolds Keywords:diffeomorphism group; infinite dimensional Lie groups PDFBibTeX XMLCite \textit{J. Grabowski}, Fundam. Math. 131, No. 2, 103--121 (1988; Zbl 0666.58011) Full Text: DOI EuDML