Symplectic topology

In mathematics, a symplectomorphism or symplectic map is an isomorphism in the category of symplectic manifolds. In classical mechanics, a symplectomorphism represents a transformation of phase space that is volume-preserving and preserves the symplectic structure of phase space, and is called a canonical transformation.

symplectic topology tool

invariant in symplectic topology and algebraic geometry

smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy–Riemann equation

in symplectic topology, the theorem that every area-preserving, orientation-preserving homeomorphism of an annulus that rotates the two boundaries in opposite directions has at least two fixed points