Residues and secondary classes for subfoliations
type: Item
instance of: scholarly article
title: Residues and secondary classes for subfoliations
zbMATH Open document ID: 0796.53027
DOI: 10.1016/0926-2245(94)00006-9
author: Demetrio Domínguez
published in: Differential Geometry and its Applications
publication date: 1994-09-20T00:00:00Z
review text: We present a theory of residues for subfoliations and relate these residues to the secondary characteristic classes for subfoliations. The method used is a generalization of Heitsch's theory of residues for foliations. We compute examples which show that certain universal secondary characteristic classes for subfoliations of codimension \((q_ 1,q_ 2)\) vary linearly independently. These results show that the homology group \(H_{2q_ 2+ 2}(B\Gamma_{(q_ 1,q_ 2)};\mathbb{Z})\) of the Haefliger classifying space \(B\Gamma_{(q_ 1,q_ 2)}\) for subfoliations of codimension \((q_ 1,q_ 2)\) admits an epimorphism onto Euclidean space. The classes considered do not belong to the subalgebra of \(H^*(B\Gamma_{(q_ 1,q_ 2)}; \mathbb{R})\) generated by the union of the universal characteristic classes for foliations of codimension \(q_ 1\) and \(q_ 2\) respectively.
Mathematics Subject Classification ID: 53C12
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 57R20
zbMATH DE Number: 567792
zbMATH Keywords: foliations
zbMATH Keywords: subfoliations
zbMATH Keywords: residues
zbMATH Keywords: secondary characteristic classes
zbMATH Keywords: Haefliger classifying space
Wikidata QID: Q115362660
MaRDI profile type: Publication
full work available at URL: 0926-2245(94)00006-9
OpenAlex ID: W2093957558
cites work: Characteristic classes for symplectic foliations
cites work: Lectures on algebraic and differential topology
cites work: Characteristic homomorphism for \((F_ 1,F_ 2)\)-foliated bundles over subfoliated manifolds
cites work: Sheaves and cohomologies associated to subfoliations
cites work: Characteristic classes of subfoliations
cites work: On the characteristic classes of subfoliations
cites work: Classes caractéristiques non-triviales de sous-feuilletages localement homogènes. (Nontrivial characteristic classes of locally homogeneous subfoliations)
cites work: Classes caractéristiques non triviales des feuilles de sous- feuilletages localement homogènes. (Non-trivial characteristic classes of leaves of locally homogeneous subfoliations)
cites work: On the Linear Independence of Certain Cohomology Classes in the Classifying Space for Subfoliations
cites work: Deformations of Secondary Classes for Subfoliations
cites work: Characteristic classes of flags of foliations
cites work: Q4084975
cites work: Q5618780
cites work: Independent variation of secondary classes
cites work: Flat bundles and residues for foliations
cites work: Dual homotopy invariants of G-foliations
cites work: Homotopy characteristic classes of foliations
cites work: Foliated bundles and characteristic classes
cites work: Noncobordant foliations of 𝑆³
cites work: Characteristic classes of almost-flag structures
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description: scientific article; zbMATH DE number 567792