
Symplectic Geometry
An Introduction based on the Seminar in Bern, 1992
Birkhäuser (Publisher)
Published on 5. November 2012
Book
Paperback/Softback
XII, 244 pages
978-3-0348-7514-1 (ISBN)
Description
The seminar Symplectic Geometry at the University of Berne in summer 1992 showed that the topic of this book is a very active field, where many different branches of mathematics come tog9ther: differential geometry, topology, partial differential equations, variational calculus, and complex analysis. As usual in such a situation, it may be tedious to collect all the necessary ingredients. The present book is intended to give the nonspecialist a solid introduction to the recent developments in symplectic and contact geometry. Chapter 1 gives a review of the symplectic group Sp(n,R), sympkctic manifolds, and Hamiltonian systems (last but not least to fix the notations). The 1\Iaslov index for closed curves as well as arcs in Sp(n, R) is discussed. This index will be used in chapters 5 and 8. Chapter 2 contains a more detailed account of symplectic manifolds start ing with a proof of the Darboux theorem saying that there are no local in variants in symplectic geometry. The most important examples of symplectic manifolds will be introduced: cotangent spaces and Kahler manifolds. Finally we discuss the theory of coadjoint orbits and the Kostant-Souriau theorem, which are concerned with the question of which homogeneous spaces carry a symplectic structure.
More details
Series
Edition
Softcover reprint of the original 1st ed. 1994
Language
English
Place of publication
Basel
Switzerland
Publishing group
Springer Basel
Target group
Professional and scholarly
Research
Illustrations
XII, 244 p.
Dimensions
Height: 203 mm
Width: 133 mm
Thickness: 15 mm
Weight
296 gr
ISBN-13
978-3-0348-7514-1 (9783034875141)
DOI
10.1007/978-3-0348-7512-7
Schweitzer Classification
Other editions
Additional editions
Beat Aebischer | Matthias Borer | Markus Kälin
Symplectic Geometry
An Introduction based on the Seminar in Bern, 1992
Book
07/1994
Birkhäuser Verlag GmbH
€45.00
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Content
1 Introduction.- 2 Darboux' Theorem and Examples of Symplectic Manifolds.- 3 Generating Functions.- 4 Symplectic Capacities.- 5 Floer Homology.- 6 Pseudoholomorphic Curves.- 7 Gromov's Compactness Theorem from a Geometrical Point of View.- 8 Contact structures.- A Generalities on Homology and Cohomology.- A.1 Axioms for homology.- A.2 Axioms for cohomology.- A.3 Homomorphisms of (co)homology sequences.- A.4 The (co)homology sequence of a triple.- A.5 Homotopy equivalence and contractibility.- A.6 Direct sums.- A.7 Triads.- A.8 Mayer-Vietoris sequence of a triad.- References.