Embedding Problems in Symplectic Geometry
Description
Symplectic geometry is the geometry underlying Hamiltonian dynamics, and symplectic mappings arise as time-1-maps of Hamiltonian flows. The spectacular rigidity phenomena for symplectic mappings discovered in the last two decades show that certain things cannot be done by a symplectic mapping. For instance, Gromov's famous "non-squeezing'' theorem states that one cannot map a ball into a thinner cylinder by a symplectic embedding. The aim of this book is to show that certain other things can be done by symplectic mappings. This is achieved by various elementary and explicit symplectic embedding constructions, such as "folding", "wrapping'', and "lifting''. These constructions are carried out in detail and are used to solve some specific symplectic embedding problems.
The exposition is self-contained and addressed to students and researchers interested in geometry or dynamics.
Reviews / Votes
"This book based on the Ph.D. thesis of the author may serve as a very good introduction to symplectic rigidity and symplectic embeddings."Iskander A. Taimanov in: Zentralblatt für Mathematik 24/2005More details
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Content
2 - Contents [Seite 9]
3 - Introduction [Seite 11]
4 - Proof of Theorem 1 [Seite 33]
5 - Proof of Theorem 2 [Seite 41]
6 - Multiple symplectic folding in four dimensions [Seite 62]
7 - Symplectic folding in higher dimensions [Seite 92]
8 - Proof of Theorem 3 [Seite 117]
9 - Symplectic wrapping [Seite 159]
10 - Proof of Theorem 4 [Seite 172]
11 - Packing symplectic manifolds by hand [Seite 198]
12 - Appendix [Seite 225]
13 - Backmatter [Seite 251]
