On the boundedness of equivariant homeomorphism groups - Jacek Lech; Ilona Michalik; Tomasz Rybicki (Opuscula Mathematica, 2018)
Given a principal \(G\)-bundle \(π:M→ B\), 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.