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Geometry, Topology, and Dynamics
Edited by: François Lalonde, University of Quebec at Montreal, QC, Canada
A co-publication of the AMS and Centre de Recherches Mathématiques.
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CRM Proceedings & Lecture Notes
1998; 148 pp; softcover
Volume: 15
ISBN-10: 0-8218-0877-X
ISBN-13: 978-0-8218-0877-1
List Price: US$43
Member Price: US$34.40
Order Code: CRMP/15
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This volume contains the proceedings from the workshop on "Geometry, Topology and Dynamics" held at CRM at the University of Montreal. The event took place at a crucial time with respect to symplectic developments. During the previous year, Seiberg and Witten had just introduced the famous gauge equations. Taubes then extracted new invariants that were shown to be equivalent in some sense to a particular form of Gromov invariants for symplectic manifolds in dimension 4. With Gromov's deformation theory, this constitutes an important advance in symplectic geometry by furnishing existence criteria.

Meanwhile, contact geometry was rapidly developing. Using both holomorphic arguments in symplectizations of contact manifolds and ad hoc topological arguments--or even gauge theoretic methods--several results were obtained on 3-dimensional contact manifolds and new surprising facts were derived about the Bennequin-Thurston invariant.

Furthermore, a fascinating relation exists between Hofer's geometry, pseudoholomorphic curves and the \(K\)-area recently introduced by Gromov. Finally, longstanding conjectures on the flux were resolved in a substantial number of specific cases by comparing various aspects of Floer-Novikov homology with Morse homology.

The papers in this volume are written by leading experts and are all clear, comprehensive, and original. The work covers a complete range of exciting new developments in symplectic and contact geometries.

Titles in this series are co-published with the Centre de Recherches Mathématiques.

Readership

Graduate students, research mathematicians, and physicists working in model theory.

Table of Contents

  • A. Banyaga -- Isomorphisms between classical diffeomorphism groups
  • Y. Eliashberg and M. J. Fraser -- Classification of topologically trivial Legendrian knots
  • H. Geiges and C. B. Thomas -- Contact structures on 7-manifolds
  • F. Lalonde, D. McDuff, and L. Polterovich -- On the flux conjectures
  • V. Lizan -- About the bubbling off phenomenon in the limit of a sequence of \(J\)-curves
  • J. D. McCarthy and J. G. Wolfson -- Symplectic resolution of isolated algebraic singularities
  • D. Milinković and Y.-G. Oh -- Generating functions versus action functional--stable Morse theory versus Floer theory
  • M. Min-oo -- Scalar curvature rigidity of certain symmetric spaces
  • K. F. Siburg -- Bi-invariant metrics for symplectic twist mappings on \(boldsymbol{T}^* \mathbb{T}^n\) and an application in Aubry-Mather theory
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