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arXiv · 2411.11422

On certain $C^0$-aspects of contactomorphism groups

Baptiste Serraille·Vukašin Stojisavljević
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Abstract

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.

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Baptiste Serraille, Vukašin Stojisavljević. 2024-11-18. On certain $C^0$-aspects of contactomorphism groups. https://arxiv.org/abs/2411.11422

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