# Symplectic Manifolds

### Some articles on symplectic manifolds, symplectic manifold, manifolds, symplectic, manifold:

Aspherical Space - Symplectically Aspherical Manifolds
... If one deals with symplectic manifolds, the meaning of "aspherical" is a little bit different ... Specifically, we say that a symplectic manifold (M,ω) is symplectically aspherical if and only if for every continuous mapping where denotes the first Chern class of an almost complex structure ... By Stokes' theorem, we see that symplectic manifolds which are aspherical are also symplectically aspherical manifolds ...
Floer Homology of Three-manifolds - Embedded Contact Homology
... Michael Hutchings, is an invariant of 3-manifolds (with a distinguished second homology class, corresponding to the choice of a spinc structure in Seiberg–Wi ... invariant, known to be equivalent to the Seiberg–Witten invariant, from closed symplectic 4-manifolds to certain non-compact symplectic 4-manifolds (namely, a contact three-manifold cross R) ... Its construction is analogous to symplectic field theory, in that it is generated by certain collections of closed Reeb orbits and its differential counts certain holomorphic curves with ends at ...
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 submanifold, often called a fiber sum ... The symplectic sum is the inverse of the symplectic cut, which decomposes a given manifold into two pieces ...
Differential Geometers - Branches of Differential Geometry - Symplectic Geometry
... Symplectic geometry is the study of symplectic manifolds ... An almost symplectic manifold is a differentiable manifold equipped with a smoothly varying non-degenerate skew-symmetric bilinear form on each tangent space, i.e ... a nondegenerate 2-form ω, called the symplectic form ...