Publisher's Synopsis
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.
