Publication
Title
The Arnold conjecture for singular symplectic manifolds
Author
Abstract
In this article, we study the Hamiltonian dynamics on singular symplectic manifolds and prove the Arnold conjecture for a large class of -symplectic manifolds. Novel techniques are introduced to associate smooth symplectic forms to the original singular symplectic structure, under some mild conditions. These techniques yield the validity of the Arnold conjecture for singular symplectic manifolds across multiple scenarios. More precisely, we prove a lower bound on the number of 1-periodic Hamiltonian orbits for -symplectic manifolds depending only on the topology of the manifold. Moreover, for -symplectic surfaces, we improve the lower bound depending on the topology of the pair (M, Z). We then venture into the study of Floer homology to this singular realm and we conclude with a list of open questions.
Language
English
Source (journal)
Journal of fixed point theory and applications. - Basel, 2007, currens
Publication
Basel : 2024
ISSN
1661-7738 [print]
1661-7746 [online]
DOI
10.1007/S11784-024-01105-Y
Volume/pages
26 :2 (2024) , p. 1-60
Article Reference
16
ISI
001205112000001
Full text (Publisher's DOI)
Full text (open access)
UAntwerpen
Faculty/Department
Research group
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identifier
Creation 02.05.2024
Last edited 08.05.2024
To cite this reference