Symplectic Aspects of the Hilbert-Smith Conjecture and p-adic Actions

Egor Shelukhin presents cases of the Hilbert–Smith conjecture for group actions by homeomorphisms with symplectic structure. The results exclude faithful actions of the additive p-adic group in this setting and give additional restrictions on group actions in symplectic topology. The argument combines a new approach to these action problems with power operations in Floer cohomology and quantitative methods in symplectic topology.