Lectures on symplectic geometry
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or exte…
Read More ↓Title Statements
- Full title :Lectures on symplectic geometry / Ana Cannas da Silva.
Summary
The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.
Read More ↓Edition Statements
- Publication Date:©2008.
- Edition:Corr. 2nd print
Publication Statements
- Publisher(s):Springer
- Place of Publication:Berlin
- Language:eng
- Publication Date:©2008.
The Physical Object
- Description:1 online resource (xiv, 247 pages) : : illustrations
Edition Identifiers
- ISBN:9783540453307, 354045330X, 3540421955, 9783540421955
- oclc:ocn304104510
- LC Classification:QA3
- Dewey Decimal:516.36
Table of Contents
pt. 1. Symplentic manifolds -- pt. 2. Symplectomorphisms -- pt. 3. Local forms -- pt. 4. Contact manifolds -- pt. 5. Compatible almost complex structures -- pt. 6. Kähler manifolds -- pt. 7. Hamiltonian mechanics -- pt. 8. Moment maps -- pt. 9. Symplectic reduction -- pt. 10. moment maps revisited -- pt. 11. Symplectic toric manifolds.
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