Quillen’s Relative Chern Character Is Multiplicative

Quillen’s Relative Chern Character Is Multiplicative Paul-emile Paradan and Michèle Vergne

Super-connections and non-commutative geometry

We show that Quillen’s formalism for computing the Chern character of the index using superconnections extends to arbitrary operators with functional calculus. We thus remove the condition that the operators have, up to homotopy, a gap in the spectrum. This is proved using differential graded algebras and non-commutative differential forms. Our results also give a new proof of the coincidence o...

Connes-Chern character in relative K-homology

Lecture 1 (Pflaum): Title: Relative cohomology and its pairings Relative cyclic cohomology theory and its pairings turned out to be a powerful tool to explain crucial properties of certain invariants in global analysis such as for example the divisor flow. In this talk, the homological foundations for pairings in relative cyclic cohomology will be explained. Moreover, the relative Chern-charact...

Strong Connections and the Relative Chern-galois Character for Corings

The Chern-Galois theory is developed for corings or coalgebras over non-commutative rings. As the first step the notion of an entwined extension as an extension of algebras within a bijective entwining structure over a non-commutative ring is introduced. A strong connection for an entwined extension is defined and it is shown to be closely related to the Galois property and to the equivariant p...

The Gauss-Bonnet-Chern Theorem on Riemannian Manifolds

This expository paper contains a detailed introduction to some important works concerning the Gauss-Bonnet-Chern theorem. The study of this theorem has a long history dating back to Gauss’s Theorema Egregium (Latin: Remarkable Theorem) and culminated in Chern’s groundbreaking work [14] in 1944, which is a deep and wonderful application of Elie Cartan’s formalism. The idea and tools in [14] have...