Rigidity of Secondary Characteristic Classes

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dc.creatorLodder, Jerry
dc.date1999-04-22
dc.date.accessioned2026-07-07T05:28:48Z
dc.date.available2026-07-07T05:28:48Z
dc.descriptionIn this paper we study the variability and rigidity of secondary characteristic classes which arise from flat connections on a manifold. Considering the connection as a Lie-algebra valued one-form, we study the characteristic map from Lie algebra cohomology to de Rham cohomology of the manifold, and prove that if the Leibniz cohomology of the Lie algebra vanishes, then all secondary characteristic classes are rigid. In the case of codimension one foliations (with trivial normal bundle), we show that a characteristic map from the Leibniz cohomology of formal vector fields to the de Rham cohomology of the manifold detects a one-parameter variation of the Godbillon-Vey class. Recall that Leibniz cohomology groups are invariants of Lie algebras defined by J-L. Loday.
dc.description15 pages
dc.identifierhttps://arxiv.org/abs/math/9904131
dc.identifierhttp://arxiv.org/abs/math/9904131
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78395
dc.subjectDifferential Geometry
dc.subjectAlgebraic Topology
dc.subjectGeometric Topology
dc.subjectK-Theory and Homology
dc.subject53 (primary), 55, 18 (secondary)
dc.titleRigidity of Secondary Characteristic Classes
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