TY  - JOUR
ID  - Lech2018
LB  - Lech2018
AU  - Lech, Jacek
AU  - Michalik, Ilona
AU  - Rybicki, Tomasz
TI  - On the boundedness of equivariant homeomorphism groups
ST  - On the boundedness of equivariant homeomorphism groups
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2018
VL  - 38
IS  - 3
SP  - 395
EP  - 408
DO  - https://doi.org/10.7494/OpMath.2018.38.3.395
UR  - https://doi.org/10.7494/OpMath.2018.38.3.395
AB  - 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.
KW  - principal \(G\)-manifold
KW  - equivariant homeomorphism
KW  - uniformly perfect
KW  - bounded
KW  - \(C^r\) equivariant diffeomorphism
SN  - 1232-9274
ER  -