Hofer Energy and Link Preserving Diffeomorphisms in Higher Genus
arXiv:2404.01052
Abstract
Given a pre-monotone Lagrangian link, we obtain Hofer energy estimates for Hamiltonian diffeomorphisms preserving it. Such estimates depend on the braid type of the Hamiltonian diffeomorphism only, and the natural language to talk about this phenomenon is provided by a family of norms on braid groups for surfaces with boundary. This generalises the results obtained by the first author to higher genus surfaces with boundary.
Exposition has been improved, typos fixed and a gap filled,following the referee's comments. Final version, to appear in the Journal of Modern Dynamics