Non Commutative Chern - Weil Homomorphism

Towards the Chern-weil Homomorphism in Non Commutative Differential Geometry

In this short review article we sketch some developments which should ultimately lead to the analogy of the Chern-Weil homomorphism for principle bundles in the realm of non commutative differential geometry. Principal bundles there should have Hopf algebras as structure ‘cogroups’. Since the usual machinery of Lie algebras, connection forms, etc., just is not available in this setting, we base...

Cyclic cohomology of Hopf algebras, and a non-commutative Chern-Weil theory

We give a construction of Connes-Moscovici’s cyclic cohomology for any Hopf algebra equipped with a character. Furthermore, we introduce a non-commutative Weil complex, which connects the work of Gelfand and Smirnov with cyclic cohomology. We show how the Weil complex arises naturally when looking at Hopf algebra actions and invariant higher traces, to give a non-commutative version of the usua...

TOWARDS THE CHERN - WEIL HOMOMORPHISMIN NON COMMUTATIVE DIFFERENTIAL GEOMETRYAndreas

On the Chern–weil Homomorphism in Finsler Spaces

The aim of this paper is to devise a Chern –Weil-type construction for a Finsler manifold (M,L) which is determined only by the manifold M and by the Finslerian fundamental function L.

ar X iv : m at h / 98 04 13 5 v 2 [ m at h . D G ] 2 4 A ug 1 99 8 DEGENERATE CHERN - WEIL THEORY AND EQUIVARIANT COHOMOLOGY

We develop a Chern-Weil theory for compact Lie group action whose generic stabilizers are finite in the framework of equivariant cohomology. This provides a method of changing an equivariant closed form within its cohomological class to a form more suitable to yield localization results. This work is motivated by our work [5] on reproving wall crossing formulas in Seiberg-Witten theory, where t...