Rigidity of secondary characteristic classes
type: Item
instance of: scholarly article
title: Rigidity of secondary characteristic classes
zbMATH Open document ID: 0960.57022
DOI: 10.1016/S0926-2245(00)00012-7
author: Jerry M. Lodder
published in: Differential Geometry and its Applications
publication date: 2001-05-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/9904131
review text: The topic of this paper is the rigidity of secondary characteristic classes associated to a flat connection on a differentiable manifold \(M\). Viewing the connection as a Lie algebra valued one-form for a Lie algebra \(g\), it is proven that if the Leibniz cohomology of \(g\) vanishes, then all secondary characteristic classes for \(g\) are rigid. Moreover, in the case when \(g\) is the Lie algebra of formal vector fields and \(M\) supports a family of codimension one foliations, the image of a characteristic map from \(HL^4(g)\) to \(H_{dR}^4(M)\) is computed, where \(HL^*\) denotes Leibniz cohomology and \(H_{dR}^*\) denotes de Rham cohomology.
reviewed by: Jerry M. Lodder
Mathematics Subject Classification ID: 57R32
Mathematics Subject Classification ID: 17A32
Mathematics Subject Classification ID: 57R30
zbMATH DE Number: 1485495
zbMATH Keywords: foliations
zbMATH Keywords: rigidity of characteristic classes
zbMATH Keywords: Godbillon-Vey invariant
zbMATH Keywords: Leibniz cohomology
Wikidata QID: Q115338427
MaRDI profile type: Publication
arXiv ID: math/9904131
OpenAlex ID: W2060232107
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description: scientific article