Lagrangian intersections and a conjecture of Arnol'd

Autor:	Gong, Wenmin
Rok vydání:	2021
Předmět:	Mathematics - Symplectic Geometry Mathematics - Differential Geometry Mathematics - Dynamical Systems 53D12 53D40 57R17
Druh dokumentu:	Working Paper
Popis:	We prove a degenerate homological Arnol'd conjecture on Lagrangian intersections beyond the case studied by A. Floer and H. Hofer via a new version of Lagrangian Ljusternik--Schnirelman theory. We introduce the notion of (Lagrangian) fundamental quantum factorizations and use them to give some uniform lower bounds of the numbers of Lagrangian intersections for some classical examples including Clifford tori in complex projective spaces. Additionally, we use the Lagrangian Ljusternik-Schnirelman theory to study the size of the intersection of a monotone Lagrangian with its image of a Hamiltonian diffeomorphism. Comment: Final version; keeping the last section in the first arXiv version about the degenerate Arnol'd conjecture for Hamiltonian periodic orbits and adding appendices A&B
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2111.15442 Zobrazit plný text záznamu View this record from Arxiv