Bourgeois, Frédéric, Colin, Vincent, Stipsicz, András (Eds.)
2014, XIII, 530 p. 164 illus., 82 illus. in color.
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Explains the application of symplectic and contact geometry to various fields of physics
Presents a wide panorama of hot topics in a very active field of mathematics
Displays tutorial-like lectures designed to be accessible to graduate students
Includes recent advances that are not covered elsewhere in the literature
Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.
Content Level »Research
Keywords »Bordered Heegaard Floer Homology - Fukaya Categories - Homological Invariants - Low-dimensional Topology - Symplectic and Contact Geometry to Various Holomorphic Curves - knot Contact Homology and Applications