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arXiv · 1609.09192

A C^0 counterexample to the Arnold conjecture

Lev Buhovsky·Vincent Humilière·Sobhan Seyfaddini
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Abstract

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 the manifold. 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.

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Lev Buhovsky, Vincent Humilière, Sobhan Seyfaddini. 2016-09-29. A C^0 counterexample to the Arnold conjecture. https://doi.org/10.1007/s00222-018-0797-x

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