On the boundedness of equivariant homeomorphism groups
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 struct...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2018-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol38/3/art/opuscula_math_3818.pdf |
| _version_ | 1818410573081083904 |
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| author | Jacek Lech Ilona Michalik Tomasz Rybicki |
| author_facet | Jacek Lech Ilona Michalik Tomasz Rybicki |
| author_sort | Jacek Lech |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-14T10:17:40Z |
| format | Article |
| id | doaj.art-c68befcad37c442ea9e4113e9fc06eea |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-14T10:17:40Z |
| publishDate | 2018-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-c68befcad37c442ea9e4113e9fc06eea2022-12-21T23:06:45ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742018-01-01383395408https://doi.org/10.7494/OpMath.2018.38.3.3953818On the boundedness of equivariant homeomorphism groupsJacek Lech0Ilona Michalik1Tomasz Rybicki2AGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, PolandAGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, PolandAGH University of Science and Technology, Faculty of Applied Mathematics, al. A. Mickiewicza 30, 30-059 Krakow, PolandGiven 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.http://www.opuscula.agh.edu.pl/vol38/3/art/opuscula_math_3818.pdfprincipal \(G\)-manifoldequivariant homeomorphismuniformly perfectbounded\(C^r\) equivariant diffeomorphism |
| spellingShingle | Jacek Lech Ilona Michalik Tomasz Rybicki On the boundedness of equivariant homeomorphism groups Opuscula Mathematica principal \(G\)-manifold equivariant homeomorphism uniformly perfect bounded \(C^r\) equivariant diffeomorphism |
| title | On the boundedness of equivariant homeomorphism groups |
| title_full | On the boundedness of equivariant homeomorphism groups |
| title_fullStr | On the boundedness of equivariant homeomorphism groups |
| title_full_unstemmed | On the boundedness of equivariant homeomorphism groups |
| title_short | On the boundedness of equivariant homeomorphism groups |
| title_sort | on the boundedness of equivariant homeomorphism groups |
| topic | principal \(G\)-manifold equivariant homeomorphism uniformly perfect bounded \(C^r\) equivariant diffeomorphism |
| url | http://www.opuscula.agh.edu.pl/vol38/3/art/opuscula_math_3818.pdf |
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