Quelques calculs en corbordisme lagrangien (Q795381)

We consider the cobordism groups, defined by Arnold, of exact Lagrange immersions of compact manifolds in the standard symplectic vector space \({\mathbb{R}}^{2n}\). Due to the Gromov-Lees theorem, their computation is that of the homotopy groups of Thom spectra built on the spaces U/O in the unoriented case (and in that case the computation is due to Smith and Stong), and U/SO in the oriented case. We give a modern variant of Smith and Stong's computation, we compute the ''even part'' and give informations on the ''odd part'' in the oriented case, and compute the images of those groups in ordinary cobordism groups. We also study some examples: generators of the low-dimensional groups, and cobordism classes which can be represented by Lagrange immersions of spheres (as a corollary, spheres actually generate the rational Langrange oriented cobordism ring). We also give some applications to the enumerative theory of Lagrange singularities.