Geometry, topology, and dynamics
著者
書誌事項
Geometry, topology, and dynamics
（CRM proceedings & lecture notes, v. 15）
American Mathematical Society, c1998
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注記
Proceedings of the Workshop on Geometry, Topology, and Dynamics, held at the CRM, Université de Montréal, June 26-30, 1995
内容説明・目次
内容説明
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.
目次
Isomorphisms between classical diffeomorphism groups by A. Banyaga Classification of topologically trivial Legendrian knots by Y. Eliashberg and M. J. Fraser Contact structures on 7-manifolds by H. Geiges and C. B. Thomas On the flux conjectures by F. Lalonde, D. McDuff, and L. Polterovich About the bubbling off phenomenon in the limit of a sequence of $J$-curves by V. Lizan Symplectic resolution of isolated algebraic singularities by J. D. McCarthy and J. G. Wolfson Generating functions versus action functional--stable Morse theory versus Floer theory by D. Milinkovic and Y.-G. Oh Scalar curvature rigidity of certain symmetric spaces by M. Min-oo Bi-invariant metrics for symplectic twist mappings on $boldsymbol{T}^* \mathbb{T}^n$ and an application in Aubry-Mather theory by K. F. Siburg.
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