A generalization of manifold and its characteristic classes
type: Item
instance of: scholarly article
title: A generalization of manifold and its characteristic classes
zbMATH Open document ID: 0714.57012
DOI: 10.1007/BF01077915
publication date: 1990-01-01T00:00:00Z
review text: The notion of an \(R_ n\)-set has been introduced by the author in Funkts. Anal. Prilozh. 21, No.3, 38-52 (1987; Zbl 0632.57016). The structures of \(R_ n\)-sets may be defined on the sets of transitivity classes of local diffeomorphisms on n-manifolds and on the sets of leaves of foliations of codimension n. The characteristic classes of \(R_ n\)- sets are obtained by using the cohomologies \(H^*(W_ n)\), \(H^*(W_ n,GL_ n)\), \(H^*(W_ n,O(n))\), where \(W_ n\) is the Lie algebra of formal vector fields on \({\mathbb{R}}^ n\), \(GL_ n=GL(n,R)\), \(O(n)=the\) orthogonal group. The Pontryagin classes and the classes induced by the characteristic classes of foliations may be found among these characteristic classes. The Pontryagin classes are real but are no longer integer valued. The introduced characteristic classes are not trivial in the case of \(H^*(W_ 1,GL_ 1)\).
reviewed by: Vasile Oproiu
Mathematics Subject Classification ID: 57R20
Mathematics Subject Classification ID: 57R30
Mathematics Subject Classification ID: 58H05
Mathematics Subject Classification ID: 58A99
zbMATH DE Number: 4176016
zbMATH Keywords: transitivity classes of local diffeomorphisms on n-manifolds
zbMATH Keywords: leaves of foliations
zbMATH Keywords: characteristic classes of \(R_ n\)-sets
zbMATH Keywords: Lie algebra of formal vector fields
zbMATH Keywords: characteristic classes of foliations
author: Mark V. Losik
MaRDI profile type: Publication
cites work: Q5801829
cites work: Q3769632
cites work: Q5677789
cites work: Feuilletages sur les variétés ouvertes
cites work: Q3756167
full work available at URL: https://doi.org/10.1007/bf01077915
OpenAlex ID: W2070238604
published in: Functional Analysis and Its Applications
description: scientific article; zbMATH DE number 4176016