##  [Symplectic Geometry](/index.php/symplectic-geometry) 

  ##  [Symplectic Geometry](https://puremath.quantumdictionary.io/symplectic-geometry-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The study of even-dimensional smooth manifolds equipped with a closed nondegenerate 2-form (a symplectic form) and the properties of diffeomorphisms that preserve that form, with deep connections to Hamiltonian mechanics, Poisson brackets and conservation laws.