Symplectic geometry and topology (Q5890287)

This survey article takes the reader on a fascinating journey through the world of symplectic and contact geometry/topology. The voyage proceeds almost without effort through this deep and vast subject. In true geometric spirit no formulas are used to present even highly nontrivial ideas and results. Starting from familiar territory, symplectic structures, Lagrangian submanifolds, Hamiltonian systems etc. the reader is immediately immersed into the rich world of caustics, wavefronts, Lagrangian singularities and their classification to arrive at the Giventhal classification theorem.NEWLINENEWLINENEWLINEIn the next section the odd (dimensional) sister world of symplectic geometry is explored: contact manifolds, projective duality, Legendrian submanifolds and fibrations, and singularities. From Huygens principle to Legendrian singularities and Euclidean reflection groups.NEWLINENEWLINENEWLINEThe last part of the survey is devoted to symplectic/contact topology. It provides insights into intersections, Floer homology, quantization conditions, Lagrange Grassmannian, Maslov index, and cobordisms, and Gromov no imbedding theorem. Finally, the reader arrives at a grand outlook over a wide area of all mathematics seen through a unifying glass of symplectic/contact geometry.NEWLINENEWLINENEWLINEThis is a breathtaking exploration for the nonspecialist while the specialist can find various ideas to widen the horizon of his own subject.