Symplectic fixed points and holomorphic spheres

1989/12/01 by Andreas Floer · 261 citations
Mathematics · #Diffeomorphism #Fixed point #Geometric and Algebraic Topology #Geometry and complex manifolds #Hamiltonian system #Holomorphic function #Homotopy and Cohomology in Algebraic Topology #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Moment map #Pure mathematics #Symplectic geometry #Symplectic manifold #Symplectic representation #Symplectomorphism

paper · doi:10.1007/bf01260388

published in Communications In Mathematical Physics 120(4), 575-611 (Springer Science and Business Media LLC)

crossref issued 1989/12/01 · crossref published 1989/12/01 · crossref published-print 1989/12/01 · openalex publication_date 1989/12/01 · crossref created 2005/03/24 · crossref deposited 2020/04/06 · openalex created_date 2025/10/10 · crossref indexed 2026/07/14 · openalex updated_date 2026/07/29

Citations

• Witten's complex and infinite-dimensional Morse theory
• Morse theory for Lagrangian intersections
• An instanton-invariant for 3-manifolds
• Reduction of symplectic manifolds with symmetry
• Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
• Supersymmetry and Morse theory
• The Index of Elliptic Operators: I

Cited by

• Symplectically aspherical Kähler manifolds, scalar curvature, and the fundamental group
• Two-boost problem for the rotating Kepler problem
• The strong Arnol'd chord conjecture for the boundary of a uniformly convex domain in ℝ⁴
• Estimate of Periodic Orbits of Degenerate Hamiltonians
• Computation of annular capacity by Hamiltonian Floer theory of non-contractible periodic trajectories
• The kei word metric on the transvection group and its unit ball
• A Short History of the Weinstein Conjecture
• Floer theory and low dimensional topology
• A Lagrangian Piunikhin-Salamon-Schwarz Morphism and Two Comparison Homomorphisms in Floer Homology
• Symplectic Floer homology of area-preserving surface diffeomorphisms
• Higher Maslov indices
• Quantum cohomology of flag manifolds and Toda lattices
• An open string analogue of Viterbo functoriality
• Floer homology [wikipedia]