Explicit symplectic packings

Nearly four centuries of research have recently confirmed that the pattern in which fruit merchants stack their oranges for market is indeed the optimal choice – if you happen to own infinitely many oranges. The corresponding problem with a finite number of objects defines an important family of invariants when transported to symplectic topology: the ball packing widths. Symplectic geometry is distinguished from volume geometry by its embedding obstructions, which are exposed by the ball packing widths. Although these invariants can be implicitly computed for some important manifolds, explicit constructions are required to develop a geometric understanding of the nature of symplectic embeddings. This problem is addressed by the present book, whose main part discusses methods that admit explicit constructions. The previously established approaches of deformation and wrapping are shortly reviewed, and then thoroughly analyzed to determine their potential and limitations. With the introduction of symplectic tunnelling, a new effective method is then added to the toolbox.