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**Embedding problems in symplectic geometry.**
*(English)*
Zbl 1073.53117

de Gruyter Expositions in Mathematics 40. Berlin: Walter de Gruyter (ISBN 3-11-017876-1/hbk). x, 250 p. (2005).

This book based on the Ph.D. thesis of the author may serve as a very good introduction to symplectic rigidity and symplectic embeddings. As it is stressed in the Preface “the aim of this book is to describe several elementary and explicit symplectic embedding constructions, such as symplectic folding’, symplectic wrapping and symplectic lifting, and this aim was achieved by expositions of these constructions in detail and by demonstrations of their applications to solving some specific problems of symplectic geometry. In particular, the author exposes the proof of his results on symplectic embeddings of ellipsoids into balls (therewith theorem 1 provides obstructions and, in its turn theorem 2 provides embeddings) [see also F. Schlenk, Isr. J. Math. 138, 215–252 (2003; Zbl 1056.53057)].

Contents: 1. Introduction. 2. Proof of theorem 1. 3. Proof of theorem 2. 4. Multiple symplectic folding in four dimensions. 5. Symplectic folding in higher dimensions. 6. Proof of theorem 3. 7. Symplectic wrapping. 8. Proof of theorem 4. 9. Packing symplectic manifolds by hands. Appendix.

Contents: 1. Introduction. 2. Proof of theorem 1. 3. Proof of theorem 2. 4. Multiple symplectic folding in four dimensions. 5. Symplectic folding in higher dimensions. 6. Proof of theorem 3. 7. Symplectic wrapping. 8. Proof of theorem 4. 9. Packing symplectic manifolds by hands. Appendix.

Reviewer: Iskander A. Taimanov (Novosibirsk)

### MSC:

53D35 | Global theory of symplectic and contact manifolds |

53-02 | Research exposition (monographs, survey articles) pertaining to differential geometry |

53D05 | Symplectic manifolds (general theory) |

52C17 | Packing and covering in \(n\) dimensions (aspects of discrete geometry) |

57R17 | Symplectic and contact topology in high or arbitrary dimension |