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The surgery of Lagrange submanifolds. (English) Zbl 0754.57027
The work can be considered as an attempt to generalize the results of F. Lalonde and J.-C. Sikorav (1989) [Comment. Math. Helv. 66, No. 1, 18-33 (1991)] who invented Lagrange surgery for surfaces. The following aspects of the existence question for Lagrange embeddings are discussed: what manifolds admit a Lagrange embedding into \(\mathbb{C}^ n\), given a symplectic manifold; what middle-dimensional homology classes can be represented by a Lagrange embedding? New characteristic classes of a generic Lagrange immersion \(f: L\to \mathbb{C}^ n\) are constructed by using a Lagrange surgery. New constructions of embedded Lagrange submanifolds of \(\mathbb{C}^{2k}\) \((k>1)\) are presented which are diffeomorphic to \(S^{2k-1}\times S^ 1\) and belong to different connected components of the space of Lagrange immersions.

MSC:
57R40 Embeddings in differential topology
57R65 Surgery and handlebodies
37J99 Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems
57R95 Realizing cycles by submanifolds
57R20 Characteristic classes and numbers in differential topology
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References:
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