On certain $C^0$-aspects of contactomorphism groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915024552853504 |
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| author | Serraille, Baptiste Stojisavljević, Vukašin |
| author_facet | Serraille, Baptiste Stojisavljević, Vukašin |
| contents | We study a number of questions related to the $C^0$-topology of contactomorphisms and contact homeomorphisms. In particular, we show a connection between Rokhlin property of contact homeomorphisms and contact non-squeezing, we define a new conjugation-invariant norm on contactomorphisms and explore its relation to the contact fragmentation norm and we introduce a measure of the size of conjugacy classes which is related to weak conjugacy equivalence. We also show that Sandon's spectral norm is $C^0$-locally bounded and extend its definition to contact homeomorphisms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_11422 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On certain $C^0$-aspects of contactomorphism groups Serraille, Baptiste Stojisavljević, Vukašin Symplectic Geometry Dynamical Systems 53D22, 37J55, 22F99 We study a number of questions related to the $C^0$-topology of contactomorphisms and contact homeomorphisms. In particular, we show a connection between Rokhlin property of contact homeomorphisms and contact non-squeezing, we define a new conjugation-invariant norm on contactomorphisms and explore its relation to the contact fragmentation norm and we introduce a measure of the size of conjugacy classes which is related to weak conjugacy equivalence. We also show that Sandon's spectral norm is $C^0$-locally bounded and extend its definition to contact homeomorphisms. |
| title | On certain $C^0$-aspects of contactomorphism groups |
| topic | Symplectic Geometry Dynamical Systems 53D22, 37J55, 22F99 |
| url | https://arxiv.org/abs/2411.11422 |