Viterbo conjecture for Zoll symmetric spaces

• 成果类型: Article
• 署名作者: Shelukhin, Egor
• 署名单位: Universite de Montreal
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-022-01124-x
• 发表日期: 2022
• 页码: 321-373
• 关键词: lagrangian submanifolds; spectral invariants; quasi-morphisms; fixed-points; symplectic hypersurfaces; hamiltonian-dynamics; Persistent Homology; mathematical-theory; holomorphic-curves; periodic-solutions

摘要

We prove a conjecture of Viterbo from 2007 on the existence of a uniform bound on the Lagrangian spectral norm of Hamiltonian deformations of the zero section in unit cotangent disk bundles, for bases given by compact rank one symmetric spaces S-n,RPn,CPn,HPn,n >= 1. We discuss generalizations and give applications, in particular to C0 symplectic topology. Our key method consists in a quantitative deformation argument for Floer persistence modules that allows to excise a divisor.