Applications of symplectic homology I

  title={Applications of symplectic homology I},
  author={Andreas Floer and Helmut Hofer and Kris Wysocki},
  journal={Mathematische Zeitschrift},
Symplectic rigidity for Anosov hypersurfaces
We prove that for a suitable (open) class of open, smoothly bounded domains in the cotangent bundle of a surface of genus $g \geq 2$ any exact symplectomorphism is homotopic to one which is smooth up
Contact orderability up to conjugation
We study in this paper the remnants of the contact partial order on the orbits of the adjoint action of contactomorphism groups on their Lie algebras. Our main interest is a class of noncompact
Spectrum estimates of Hill's lunar problem
We investigate the action spectrum of Hill's lunar problem by observing inclusions between the Liouville domains enclosed by the regularized energy hypersurfaces of the rotating Kepler problem and
The solid trefoil knot as an algebraic surface
We give an explicit polynomial of degree 14 in three real variables x, y and z such that the zero set gives the solid trefoil knot. The polynomial depends on two further parameters which enable a
On symplectic folding
We study the rigidity and flexibility of symplectic embeddings of simple shapes. It is first proved that under the condition $r_n^2 \le 2 r_1^2$ the symplectic ellipsoid $E(r_1, ..., r_n)$ with radii
Symplectic and contact differential graded algebras
We define Hamiltonian simplex differential graded algebras (DGA) with differentials that deform the high energy symplectic homology differential and wrapped Floer homology differential in the cases
The geometry of symplectic energy
"Non-Squeezing Theorem" which says that it is impossible to embed a large ball symplectically into a thin cylinder of the form R2, x B2, where B2 is a 2-disc. This led to Hofer's discovery of
On the Lagrangian capacity of convex or concave toric domains
We establish computational results concerning the Lagrangian capacity, originally defined by Cieliebak–Mohnke. More precisely, we show that the Lagrangian capacity of a 4-dimensional convex toric
Selective symplectic homology with applications to contact non-squeezing
We prove a contact non-squeezing phenomenon on homotopy spheres that are fillable by Liouville domains with infinite dimensional symplectic homology: there exists a smoothly embedded ball in such a


Morse‐type index theory for flows and periodic solutions for Hamiltonian Equations
An index theory for flows is presented which extends the classical Morse theory for gradient flows on compact manifolds. The theory is used to prove a Morse-type existence statement for periodic
Symplectic homology I open sets in ℂn
Pseudo holomorphic curves in symplectic manifolds
Definitions. A parametrized (pseudo holomorphic) J-curve in an almost complex manifold (IS, J) is a holomorphic map of a Riemann surface into Is, say f : (S, J3 ~(V, J). The image C=f(S)C V is called
Syplectic topology and Hamiltonian dynamics II
Symplectic topology as the geometry of generating functions
Symplectic topology and Hamiltonian dynamics
On etudie des applications symplectiques non lineaires. Capacites symplectiques. Construction d'une capacite symplectique. Problemes de plongement. Problemes de rigidite
On the topological properties of symplectic maps
  • H. Hofer
  • Mathematics
    Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  • 1990
Synopsis In this paper we show that symplectic maps have surprising topological properties. In particular, we construct an interesting metric for the symplectic diffeomorphism groups, which is