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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Symplectic Geometry: An Introduction Based on the Seminar in Bern, 1992

Symplectic Geometry: An Introduction Based on the Seminar in Bern, 1992

Aebischer, B.
Borer, M.
Kälin, M.

Paperback

Series: Progress in Mathematics, Book 124

General MathematicsGeometry

ISBN10: 3034875142
ISBN13: 9783034875141
Publisher: Springer Nature
Published: Nov 5 2012
Pages: 244
Weight: 0.60
Height: 0.55 Width: 5.25 Depth: 8.00
Language: English
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.

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