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Symplectic and Contact Topology: Interactions and Perspectives
Edited by: Yakov Eliashberg, Stanford University, CA, Boris Khesin, University of Toronto, ON, Canada, and François Lalonde, University of Quebec at Montreal, Canada
A co-publication of the AMS and Fields Institute.
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Fields Institute Communications
2003; 199 pp; hardcover
Volume: 35
ISBN-10: 0-8218-3162-3
ISBN-13: 978-0-8218-3162-5
List Price: US$70
Member Price: US$56
Order Code: FIC/35
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New Perspectives and Challenges in Symplectic Field Theory - Miguel Abreu, Francois Lalonde and Leonid Polterovich

The papers presented in this volume are written by participants of the "Symplectic and Contact Topology, Quantum Cohomology, and Symplectic Field Theory" symposium. The workshop was part of a semester-long joint venture of The Fields Institute in Toronto and the Centre de Recherches Mathématiques in Montreal.

The twelve papers cover the following topics: Symplectic Topology, the interaction between symplectic and other geometric structures, and Differential Geometry and Topology.

The Proceeding concludes with two papers that have a more algebraic character. One is related to the program of Homological Mirror Symmetry: the author defines a category of extended complex manifolds and studies its properties. The subject of the final paper is Non-commutative Symplectic Geometry, in particular the structure of the symplectomorphism group of a non-commutative complex plane.

The in-depth articles make this book a useful reference for graduate students as well as research mathematicians.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).

Readership

Graduate students and research mathematicians interested in geometry and topology.

Table of Contents

  • M. Abreu -- Kähler geometry of toric manifolds in symplectic coordinates
  • V. Apostolov and T. Drăghici -- The curvature and the integrability of almost-Kähler manifolds: A survey
  • F. Bourgeois -- A Morse-Bott approach to contact homology
  • J. Chen -- Deforming surfaces in four dimensional manifolds
  • A. Dancer and M. Y. Wang -- Integrability and the Einstein equations
  • J. Epstein and D. Fuchs -- On the invariants of Legendrian mirror torus links
  • R. Ibáñez, Yu. Rudyak, A. Tralle, and L. Ugarte -- Symplectically harmonic cohomology of nilmanifolds
  • D. Kotschick -- Godbillon-Vey invariants for families of foliations
  • S. A. Merkulov -- A note on extended complex manifolds
  • V. Pidstrygach -- On action of symplectomorphisms of the complex plane on pairs of matrices
  • L. Polterovich -- Slow symplectic maps, continued fractions, and related stories
  • J.-C. Sikorav -- The gluing construction for normally generic \(J\)-holomorphic curves
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