Symplectic Topology

Symplectic geometry is a branch of differential geometry and differential topology that studies symplectic manifolds; that is, differentiable manifolds equipped with a closed, nondegenerate 2-form. Symplectic geometry has its origins in the Hamiltonian formulation of classical mechanics where the phase space of certain classical systems takes on the structure of a symplectic manifold.Symplectic geometry has a number of similarities and differences with Riemannian geometry, which is the study of differentiable manifolds equipped with nondegenerate, symmetric 2-tensors (called metric tensors). Unlike in the Riemannian case, symplectic manifolds have no local invariants such as curvature.
Posts about Symplectic Topology
  • 2015 Breakthrough Prizes Winners Announced

    … of the relation between stability in algebraic geometry and in global differential geometry, both for bundles and for Fano varieties. Maxim Kontsevich, Institut des Hautes Études Scientifiques, for work making a deep impact in a vast variety of mathematical disciplines, including algebraic geometry, deformation theory, symplectic topology, homological…

    David Cohen/ AllFacebookin Google- 19 readers -
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