On the boundedness of equivariant homeomorphism groups

Opuscula Mathematica

Tomasz Rybicki¹  Jacek Lech¹  Ilona Michalik¹ 

[1] AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, Poland;

关键词: principal \(G\)-manifold;    equivariant homeomorphism;    uniformly perfect;    bounded;    \(C^r\) equivariantdiffeomorphism;   

DOI  :  https://doi.org/10.7494/OpMath.2018.38.3.395

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown