A counterexample to the Arnold conjecture

• 成果类型: Article
• 署名作者: Buhovsky, Lev; Humiliere, Vincent; Seyfaddini, Sobhan
• 署名单位: Tel Aviv University; Universite Paris Cite; Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0797-x
• 发表日期: 2018
• 页码: 759-809
• 关键词: fixed-point theorem; symplectic-manifolds; hamiltonian homeomorphisms; lagrangian intersections; geometry; c-0-rigidity; EQUATIONS; TOPOLOGY; SURFACES; FLOWS

摘要

The Arnold conjecture states that a Hamiltonian diffeomorphism of a closed and connected symplectic manifold must have at least as many fixed points as the minimal number of critical points of a smooth function on M. It is well known that the Arnold conjecture holds for Hamiltonian homeomorphisms of closed symplectic surfaces. The goal of this paper is to provide a counterexample to the Arnold conjecture for Hamiltonian homeomorphisms in dimensions four and higher. More precisely, we prove that every closed and connected symplectic manifold of dimension at least four admits a Hamiltonian homeomorphism with a single fixed point.