Dehn-Seidel twist, $C^0$ symplectic topology and barcodes
Abstract
We initiate the study of the symplectic mapping class group, i.e. the group of isotopy classes of symplectic homeomorphisms. We prove that none of the different powers of the square of the Dehn-Seidel twist belong to the same connected component of the group of symplectic homeomorphisms of certain Liouville domains. This generalizes to the setting a celebrated result of Seidel. In other words, we obtain the non-triviality of the symplectic mapping class group in these domains and in fact an element of infinite order. For that purpose, we develop a method coming from Floer theory and the theory of barcodes. This builds on recent developments of -symplectic topology. In particular, we adapt and generalize to our context results by Buhovsky-Humili\`ere-Seyfaddini and Kislev-Shelukhin.
Keywords
Cite
@article{arxiv.2101.07878,
title = {Dehn-Seidel twist, $C^0$ symplectic topology and barcodes},
author = {Alexandre Jannaud},
journal= {arXiv preprint arXiv:2101.07878},
year = {2021}
}