\(J\)-holomorphic curves and symplectic topology
type: Item
instance of: scholarly article
zbMATH Open document ID: 1272.53002
author: Dusa McDuff
author: Dietmar A. Salamon
publication date: 2012-07-10T00:00:00Z
Mathematics Subject Classification ID: 53-02
Mathematics Subject Classification ID: 53D05
Mathematics Subject Classification ID: 53D45
Mathematics Subject Classification ID: 53D35
Mathematics Subject Classification ID: 57R17
Mathematics Subject Classification ID: 37J05
Mathematics Subject Classification ID: 58J05
zbMATH DE Number: 6054087
zbMATH Keywords: holomorphic curves
zbMATH Keywords: symplectic topology
zbMATH Keywords: symplectic geometry
MaRDI profile type: Publication
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title: \(J\)-holomorphic curves and symplectic topology
published in: Colloquium Publications. American Mathematical Society
review text: This book is the second edition of [Zbl 1064.53051] written by two top specialists on this field. As said in the preface to this edition, the main purpose of it is to correct various errors in the first edition and to update the discussions of current work in the field.NEWLINENEWLINEThe main change of Chapter 1 is that two passages (``Applications'' and ``Quantum cohomology'') from Section 1.4 of the first edition were extended into the new Section 1.5: Application and further developments. Here, some new references and recent relevant results are mentioned.NEWLINENEWLINEChapter 2 has no big changes. Minor errors were corrected; a few sentences, and Exercise 2.5.3 and Remark 2.5.6 were newly added.NEWLINENEWLINEIn Chapter 3, Remark 3.12 was newly added, and Section 3.4 was rewritten. Other changes are minor.NEWLINENEWLINEAs to Chapter 4, Proposition 4.1.5 was newly added, and may lead to Proposition 4.1.5 even if the almost complex structure \(J\) is only \(\omega\)-tame. Remarks 4.3.2 and 4.3.6 were newly added. But a main change is a revised form of Section 4.4, where the statement and proof of the isoparametric inequality was corrected.NEWLINENEWLINEIn Chapter 5, the proofs of Theorem 5.2.2 and Theorem 5.3.1 became clearer and more rigorous. Remark 5.2.3 and Exercise 5.3.3 were newly added.NEWLINENEWLINEThe main changes of Chapter 6 is to make the proof of Theorem 6.2.6(II) clearer and more rigorous.NEWLINENEWLINEIn Chapter 7, the proofs of Theorem 7.2.3 and Proposition 7.4.8 were rewritten. In addition, Exercise 7.2.4 was newly added.NEWLINENEWLINEIn Chapter 8, the authors added Example 8.4.3 and Remark 8.6.13, where some relevant developments and work were mentioned.NEWLINENEWLINEChapter 9 reviews many applications in symplectic topology. Some of them are proved in detail, but most of the important results were only outlined or the references of these results are pointed out.NEWLINENEWLINEIn Chapter 10, Section 10.9 was newly added. It is shown for an almost co…
reviewed by: Guangcun Lu
description: scientific article; zbMATH DE number 6054087