@Article{Lech2018,
author = "Lech, Jacek and Michalik, Ilona and Rybicki, Tomasz",
title = "On the boundedness of equivariant homeomorphism groups",
journal = "Opuscula Math.",
year = "2018",
volume = "38",
number = "3",
pages = "395--408",
doi = "https://doi.org/10.7494/OpMath.2018.38.3.395",
url = "https://doi.org/10.7494/OpMath.2018.38.3.395",
abstract = "Given a principal \(G\)-bundle \(\pi:M\to B\), let \(\mathcal{H}_G(M)\) be the identity component of the group of \(G\)-equivariant homeomorphisms on \(M\). The problem of the uniform perfectness and boundedness of \(\mathcal{H}_G(M)\) is studied. It occurs that these properties depend on the structure of \(\mathcal{H}(B)\), the identity component of the group of homeomorphisms of \(B\), and of \(B\) itself. Most of the obtained results still hold in the \(C^r\) category.",
keywords = "principal \(G\)-manifold, equivariant homeomorphism, uniformly perfect, bounded, \(C^r\) equivariant diffeomorphism",
issn = "1232-9274"
}