Intrinsic characteristic classes of a local Lie group

Secondary Characteristic Classes of Lie Algebra Extensions

We introduce a notion of secondary characteristic classes of Lie algebra extensions. As a spin-off of our construction we obtain a new proof of Lecomte’s generalization of the Chern–Weil homomorphism.

Topology of Lie Groups and Characteristic Classes

Characteristic Classes of Lie Algebroid Morphisms

We extend R. Fernandes’ construction of the secondary characteristic classes of a Lie algebroid to the case of a base-preserving morphism between two Lie algebroids. Like in the case of a Lie algebroid, the simplest characteristic class of our construction coincides with the modular class of the morphism. In [4] R. Fernandes has constructed a sequence of secondary characteristic classes of a Li...

Lie Algebroids, Holonomy and Characteristic Classes

We extend the notion of connection in order to study singular geometric structures, namely, we consider a notion of connection on a Lie algebroid which is a natural extension of the usual concept of a covariant connection. It allows us to define holonomy of the orbit foliation of a Lie algebroid and prove a Stability Theorem. We also introduce secondary or exotic characteristic classes, thus pr...

Characteristic Classes and Representations of Discrete Subgroups of Lie Groups

A volume invariant is used to characterize those representations of a countable group into a connected semisimple Lie group G which are injective and whose image is a discrete cocompact subgroup of G. Let IT be a discrete cocompact subgroup of G and consider the analytic variety Hom(7r, G) consisting of homomorphisms 0: TT —> G. Denote by K a maximal compact subgroup of G and X = K\G the associ...