Symplectic topology

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. Together the symplectic sum and cut may be viewed as a deformation of symplectic manifolds, analogous for example to deformation to the normal cone in algebraic geometry. The symplectic sum has been used to construct previously unknown families of symplectic manifolds, and to derive relationships among the Gromov–Witten invariants of symplectic manifolds. (Wikipedia).

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Ever wondered what a partial sum is? The simple answer is that a partial sum is actually just the sum of part of a sequence. You can find a partial sum for both finite sequences and infinite sequences. When we talk about the sum of a finite sequence in general, we’re talking about the sum

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From playlist Approximating Area Under a Curve

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Related pages

Normal bundle | Cohomology | Quotient space (topology) | Transversality (mathematics) | Ambient isotopy | Symplectic cut | Euler class | Finitely presented group | Connected sum | Gromov–Witten invariant | Mathematics | Pseudoholomorphic curve | Sphere | Algebraic geometry | Identity (mathematics) | Symplectic geometry | Category (mathematics) | Blowing up | Compact space | Fundamental group | Divisor (algebraic geometry) | Fibration | Kähler manifold | Symplectic manifold