Symplectic Geometry

doi:10.1017/CBO9780511526343

This volume is based on lectures given at a workshop and conference on symplectic geometry at the University of Warwick in August 1990. The area of symplectic geometry has developed rapidly in the past ten years with major new discoveries that were motivated by and have provided links with many other subjects such as dynamical systems, topology, gauge theory, mathematical physics and singularity theory. The conference brought together a number of leading experts in these areas of mathematics. The contributions to this volume reflect the richness of the subject and include expository papers as well as original research. They will be an essential source for all research mathematicians in symplectic geometry.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Introduction
pp 1-4
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A variational interpretation of Melnikov's function and exponentially small separatrix splitting
pp 5-36
- By Sigurd Angenent, Mathematics Department, UW Madison
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Global Darboux theorems and a linearization problem
pp 37-44
- By Eleonora Ciriza, ICTP, Trieste, Italy
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Complex cobordism, Ashtekar's equations and diffeomorphisms
pp 45-56
- By S. K. Donaldson
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Instanton homology and symplectic fixed points
pp 57-94
- By Stamatis Dostoglou, Mathematics Institute, University of Warwick, Coventry CV4 7AL, Great Britain, Dietmar Salamon, Mathematics Institute, University of Warwick, Coventry CV4 7AL, Great Britain
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An energy–capacity inequality for the symplectic holonomy of hypersurfaces flat at infinity
pp 95-114
- By Y. Eliashberg, Department of Mathematics, Stanford University, California, 94305, USA, H. Hofer, Institut für Mathematik, Ruhr-Universität Bochum, 4630 Bochum, Germany
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Caustics Dk at points of interface between two media
pp 115-126
- By M. Kazarian
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Examples of singular reduction
pp 127-156
- By Eugene Lerman, Mathematisch Instituut der Rijksuniversiteit te Utrecht, PO Box 80.010, 3508 TA Utrecht, The Netherlands, Richard Montgomery, Mathematisch Instituut der Rijksuniversiteit te Utrecht, PO Box 80.010, 3508 TA Utrecht, The Netherlands, Reyer Sjamaar, Mathematisch Instituut der Rijksuniversiteit te Utrecht PO Box 80.010, 3508 TA Utrecht, The Netherlands
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Remarks on the uniqueness of symplectic blowing up
pp 157-168
- By Dusa McDuff
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The 4-dimensional symplectic camel and related results
pp 169-182
- By Dusa McDuff, Lisa Traynor
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Differential forms and connections adapted to a contact structure, after M. Rumin
pp 183-196
- By Pierre Pansu, U.R.A. 169 du C.N.R.S., Centre de Mathématiques, Ecole Polytechnique F-91128 Palaiseau, U.R.A. 1169 du C.N.R.S. Mathématiques Université Paris-Sud F-91405 Orsay
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The Maslov class rigidity and non-existence of Lagrangian embeddings
pp 197-202
- By Leonid Polterovich, Institut des Hautes Etudes Scientifiques 35, route de Chartres, 91440-BURES sur YVETTE (France)
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Phase functions and path integrals
pp 203-226
- By Joel Robbin, Mathematics Department, University of Wisconsin Madison, WI 53706 USA, Dietmar Salamon, Mathematics Institute, University of Warwick Coventry CV4 7AL Great Britain
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Symplectic mappings which are stable at infinity
pp 227-236
- By Eduard Zehnder, Eidg. Technische Hochschule, Zürich
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Symplectic Geometry

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Introduction
pp 1-4

A variational interpretation of Melnikov's function and exponentially small separatrix splitting
pp 5-36

Global Darboux theorems and a linearization problem
pp 37-44

Complex cobordism, Ashtekar's equations and diffeomorphisms
pp 45-56

Instanton homology and symplectic fixed points
pp 57-94

An energy–capacity inequality for the symplectic holonomy of hypersurfaces flat at infinity
pp 95-114

Caustics Dk at points of interface between two media
pp 115-126

Examples of singular reduction
pp 127-156

Remarks on the uniqueness of symplectic blowing up
pp 157-168

The 4-dimensional symplectic camel and related results
pp 169-182

Differential forms and connections adapted to a contact structure, after M. Rumin
pp 183-196

The Maslov class rigidity and non-existence of Lagrangian embeddings
pp 197-202

Phase functions and path integrals
pp 203-226

Symplectic mappings which are stable at infinity
pp 227-236

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Symplectic Geometry

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