Classes caractéristiques isotropes. (Isotropic characteristic classes)
type: Item
instance of: scholarly article
title: Classes caractéristiques isotropes. (Isotropic characteristic classes)
zbMATH Open document ID: 0662.55009
DOI: 10.1007/BF01443523
author: François Lalonde
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164604
review text: Let \(E\to B\) be a symplectic fiber bundle and let I,C\(\subset E\) be a pair consisting of a real isotropic subbundle of complementary dimensions. We associate to the triple (I,C,E) a classifying map with values in a stable isotropic Grassmannian \(\alpha\) : \(B\to {\mathfrak I}G(k)\). The pull-back by \(\alpha\) of the generators of the cohomology ring \(H^*({\mathfrak I}G(k);A)\) are the isotropic characteristic classes of the triple (I,C,E). We show that these classes are fine obstructions for any homomorphic deformation of the pair I, C into a pair \(I'\), \(C'\) everywhere transversal and we describe the geometric applications of this situation. Then we formulate the h-principle for isotropic immersions of a manifold into a symplectic manifold, from which we infer some consequences when the symplectic manifold is \({\mathbb{C}}^ n\) with the standard form. Finally, we compute the stable and unstable cohomologies of isotropic Grassmannians.
Mathematics Subject Classification ID: 55R40
Mathematics Subject Classification ID: 37J99
Mathematics Subject Classification ID: 57R15
Mathematics Subject Classification ID: 57R42
Mathematics Subject Classification ID: 53C15
zbMATH DE Number: 4082512
zbMATH Keywords: isotropic immersions into a symplectic manifold
zbMATH Keywords: symplectic fiber bundle
zbMATH Keywords: real isotropic subbundle
zbMATH Keywords: classifying map
zbMATH Keywords: stable isotropic Grassmannian
zbMATH Keywords: isotropic characteristic classes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4082512