Schlenk Embedding Problems in Symplectic Geometry

1. Auflage 2008
ISBN: 978-3-11-019969-7
Verlag: De Gruyter
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 40, 260 Seiten

Reihe: De Gruyter Expositions in Mathematics

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 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 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.

Zielgruppe

Research Mathematicians, Students; Academic Libraries

Autoren/Hrsg.

Schlenk, Felix

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie

Inhaltsverzeichnis

1;Frontmatter;1
2;Contents;9
3;Introduction;11
4;Proof of Theorem 1;33
5;Proof of Theorem 2;41
6;Multiple symplectic folding in four dimensions;62
7;Symplectic folding in higher dimensions;92
8;Proof of Theorem 3;117
9;Symplectic wrapping;159
10;Proof of Theorem 4;172
11;Packing symplectic manifolds by hand;198
12;Appendix;225
13;Backmatter;251

Über Autor(innen)

Felix Schlenk is Postdoc at the Department of Mathematics of Leipzig University, Leipzig, Germany.