Lectures on Symplectic Geometry (Lecture Notes in Mathematics, Band 1764) - Softcover

Cannas Da Silva, Ana Cannas

Softcover

ISBN 10: 3540421955 ISBN 13: 9783540421955

Verlag: Springer, 2001

Inhaltsangabe

Symplectic Manifolds.- Symplectic Forms.- Symplectic Form on the Cotangent Bundle.- Symplectomorphisms.- Lagrangian Submanifolds.- Generating Functions.- Recurrence.- Local Forms.- Preparation for the Local Theory.- Moser Theorems.- Darboux-Moser-Weinstein Theory.- Weinstein Tubular Neighborhood Theorem.- Contact Manifolds.- Contact Forms.- Contact Dynamics.- Compatible Almost Complex Structures.- Almost Complex Structures.- Compatible Triples.- Dolbeault Theory.- Kähler Manifolds.- Complex Manifolds.- Kähler Forms.- Compact Kähler Manifolds.- Hamiltonian Mechanics.- Hamiltonian Vector Fields.- Variational Principles.- Legendre Transform.- Moment Maps.- Actions.- Hamiltonian Actions.- Symplectic Reduction.- The Marsden-Weinstein-Meyer Theorem.- Reduction.- Moment Maps Revisited.- Moment Map in Gauge Theory.- Existence and Uniqueness of Moment Maps.- Convexity.- Symplectic Toric Manifolds.- Classification of Symplectic Toric Manifolds.- Delzant Construction.- Duistermaat-Heckman Theorems.

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Über die Autorin bzw. den Autor

Ana Cannas da Silva is a Professor in the Department of Mathematics at ETH Zurich, where she is regularly in charge of mathematics courses for scientists and engineers. She studied at technical schools, earning a PhD from MIT in Boston. Previously, she worked at the University of California, Berkeley, at IST/Técnico in Lisbon and at Princeton University. Her research focuses on symplectic geometry. Özlem Imamölu is a Professor in the Department of Mathematics at ETH Zurich. After obtaining her bachelor degree in electrical engineering in the Middle East Technical University in Ankara, she did her PhD in mathematics at the University of California, Santa Cruz. She moved to Zurich from Santa Barbara where she was a professor at the University of California. Her research focuses on number theory. Alessandra Iozzi is a Professor in the Department of Mathematics at ETH Zurich. She has been teaching regularly mathematics courses for mathematicians, scientists and engineers. She got her PhD from the University of Chicago and, before coming to ETH, she was a Professor at the University of Pennsylvania and the University of Maryland. Her research interests are in discrete subgroups of Lie groups and rigidity questions in geometric group theory.

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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.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2001
• Sprache: Englisch
• ISBN 10: 3540421955
• ISBN 13: 9783540421955
• Einband: Taschenbuch
• Anzahl der Seiten: 266
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland