Explore: Symplectic And Contact Topology

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds

geometry, a structure on certain even-dimensional manifolds. Both contact and symplectic geometry are motivated by the mathematical formalism of classical

in symplectic and contact topology, in particular for his proof of the symplectic rigidity and the development of 3-dimensional contact topology. In

mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology. Floer homology is an invariant that arises as an

Quaternion-Kähler manifold Symplectic topology Symplectic space Symplectic manifold Symplectic structure Symplectomorphism Contact structure Contact geometry Hamiltonian

\omega } , called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology. Symplectic manifolds arise naturally

role in symplectic geometry. The first result in symplectic topology is probably the Poincaré–Birkhoff theorem, conjectured by Henri Poincaré and then proved

manifold Symplectic manifold Banach manifold Fréchet manifold Hilbert manifold List of topological spaces – List of concrete topologies and topological

on Symplectic Geometry. Springer. doi:10.1007/978-3-540-45330-7. ISBN 978-3-540-42195-5. Geiges, Hansjörg (2008). An Introduction to Contact Topology. Cambridge

coordinates, and ξ i {\displaystyle \xi _{i}} odd coordinates. (An odd symplectic form should not be confused with a Grassmann-even symplectic form on a