Symplectic rigidity and weak commutativity

TL;DR

This paper offers an alternative proof of a fundamental symplectic rigidity theorem and introduces a new concept of weak Lie brackets for Hamiltonian vector fields, enhancing understanding of symplectic geometry.

Contribution

It provides a novel proof of the C^0-rigidity theorem and proposes a new notion of weak Lie brackets for Hamiltonian vector fields, advancing symplectic geometry theory.

Findings

Alternative proof of C^0-rigidity theorem

Introduction of weak Lie brackets for Hamiltonian vector fields

Comparison of new notion with existing concepts

Abstract

An alternative proof of Eliashberg-Gromov's C^0-rigidity theorem is presented and a new notion of weak Lie brackets for Hamiltonian vector fields is proposed and compared.