The number of Hamiltonian fixed points on symplectically aspherical manifolds

2016/09/15 by Georgios Dimitroglou Rizell, Rizell, Georgios Dimitroglou, Roman Golovko +1
Mathematics · #53D12 #53D42 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1609.04776

openalex publication_date 2016/09/15 · openalex created_date 2016/09/30 · openalex updated_date 2026/07/28

Abstract

We show that a generic Hamiltonian diffeomorphism on a closed symplectic manifold which is symplectically aspherical has at least the stable Morse number of fixed points - this is in line with a conjecture by Arnold.

Citations

• Floer homology of Lagrangians in clean intersection

Related

• The Conley Conjecture
• Degenerate symplectic fixed points and Gromov-Witten invariants
• On the degenerate Arnold conjecture on \mathbb T^2m× \mathbb C\mathbb Pⁿ
• Action Selectors and the Fixed Point Set of a Hamiltonian Diffeomorphism
• Franks' dichotomy for toric manifolds, Hofer-Zehnder conjecture, and gauged linear sigma model