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symplectic invariant

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  • Symplectic geometry — is a branch of differential topology/geometry which 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… …   Wikipedia

  • Symplectic sum — In mathematics, specifically in symplectic geometry, the symplectic sum is a geometric modification on symplectic manifolds, which glues two given manifolds into a single new one. It is a symplectic version of connected summation along a… …   Wikipedia

  • Gromov–Witten invariant — In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic… …   Wikipedia

  • Geometric invariant theory — In mathematics Geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces. It was developed by David Mumford in 1965, using ideas from the paper… …   Wikipedia

  • Seiberg–Witten invariant — In mathematics, Seiberg–Witten invariants are invariants of compact smooth 4 manifolds introduced by harvtxt|Witten|1994, using the Seiberg Witten theory studied by harvs|txt=yes|last=Seiberg|last2=Witten|year1=1994a|year2=1994b during their… …   Wikipedia

  • Taubes's Gromov invariant — In mathematics, the Gromov invariant of Clifford Taubes counts embedded (possibly disconnected) pseudoholomorphic curves in a symplectic 4 manifold. Taubes proved that is equivalent to the Seiberg Witten equations, in a series of four long papers …   Wikipedia

  • Arf invariant (knot) — In the mathematical field of knot theory, the Arf invariant of a knot, named after Cahit Arf, is a knot invariant obtained from a quadratic form associated to a Seifert surface. If F is a Seifert surface of a knot, then the homology group H1( F …   Wikipedia

  • Floer homology — is a mathematical tool used in the study of symplectic geometry and low dimensional topology. First introduced by Andreas Floer in his proof of the Arnold conjecture in symplectic geometry, Floer homology is a novel homology theory arising as an… …   Wikipedia

  • Orthogonal group — Group theory Group theory …   Wikipedia

  • Differential geometry — A triangle immersed in a saddle shape plane (a hyperbolic paraboloid), as well as two diverging ultraparallel lines. Differential geometry is a mathematical discipline that uses the techniques of differential and integral calculus, as well as… …   Wikipedia

  • Liouville's theorem (Hamiltonian) — In physics, Liouville s theorem, named after the French mathematician Joseph Liouville, is a key theorem in classical statistical and Hamiltonian mechanics. It asserts that the phase space distribution function is constant along the trajectories… …   Wikipedia

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