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Lagrangian embeddings and Lagrangian cobordism. (English) Zbl 0933.53038

Khovanskij, A. (ed.) et al., Topics in singularity theory. V. I. Arnold’s 60th anniversary collection. Providence, RI: American Mathematical Society. Transl., Ser. 2, Am. Math. Soc. 180(34), 13-23 (1997).
The paper is devoted to start a classification theory of Lagrangian embeddings in the symplectic vector space \((\mathbb{R}^{2n}, dp\wedge dq)\). The main tools of this approach are the Liouville class and the \(J\)-holomorphic curves of M. Gromov [Invent. Math 82, 307-347 (1985; Zbl 0592.53025)]. Also, the connection with Arnold’s celebrated theory of Lagrangian cobordism is pointed out.
For the entire collection see [Zbl 0870.00037].

MSC:

53D12 Lagrangian submanifolds; Maslov index
57R70 Critical points and critical submanifolds in differential topology

Citations:

Zbl 0592.53025
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