Summary
Our universe (space-time) has an underlying mathematical structure called a four-dimensional manifold, and yet surprisingly, we understand very little about the geometry of four-dimensional spaces. Topology studies the fundamental properties of space that remain unchanged even when the structure is continuously bent and deformed, while dynamics studies the self-mappings of the space that preserve a given structure. Initially formulated from the equations of Hamiltonian mechanics, symplectic structures have grown into an important abstract mathematical topic that is particularly powerful for st
