Free subgroups of the homeomorphism group of the reals. (English) Zbl 0604.57015

Blass, Andreas; Kister, James M.

Topology Appl. 24, 243-252 (1986).

The authors give a short self-contained proof of the known result that the homeomorphism group \({\mathcal H}({\mathbb{R}})\) of the reals contains a free subgroup of rank equal to the cardinality of the continuum. They apply similar techniques to show that, in many cases, a subgroup G of \({\mathcal H}({\mathbb{R}})\) can be enlarged by the choice of an independent generator h to get a subgroup of \({\mathcal H}({\mathbb{R}})\) isomorphic to the free product G* \({\mathbb{Z}}\), and to give criteria for the existence of many (in the sense of a comeager set in a natural complete metric topology) homeomorphisms h independent of G.

Reviewer: T.Nôno

MSC:

57N99	Topological manifolds
57S25	Groups acting on specific manifolds
58D05	Groups of diffeomorphisms and homeomorphisms as manifolds

Keywords:

compact metric topology; homeomorphism group of the reals; free subgroup; comeager set

References:

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