On the Hofer-Zehnder conjecture

• 成果类型: Article
• 署名作者: Shelukhin, Egor
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2022.195.3.1
• 发表日期: 2022
• 页码: 775-839
• 关键词: noncontractile periodic-orbits; fixed-point theorem; local floer homology; hamiltonian-dynamics; subharmonic solutions; spectral invariants; mathematical-theory; arnold conjecture; morse-theory; persistence

摘要

We prove that if a Hamiltonian diffeomorphism of a closed monotone symplectic manifold with semisimple quantum homology has more contractible fixed points, counted homologically, than the total dimension of the homology of the manifold, then it must have an infinite number of contractible periodic points. This constitutes a higher-dimensional homological generalization of a celebrated result of Franks from 1992, as conjectured by Hofer and Zehnder in 1994.