First Draft AN ALGEBRAIC GEOMETRIC REALIZATION OF THE CHERN CHARACTER

An Algebraic Geometric Realization of the Chern Character

ar X iv : 0 80 8 . 01 83 v 1 [ m at h . D G ] 1 A ug 2 00 8 RELATIVE CHERN CHARACTER , BOUNDARIES AND INDEX FORMULÆ

For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have ‘geometric K-theory’, namely the ‘transmission algebra’ introduced by Boutet de Monvel [5], the ‘zero algebra’ introduced by Mazzeo in [9, 10] and the ‘scattering algebra’ from [16] we give explicit formulæ for the Chern character of the index bundle in terms of the symbols (including norma...

Relative Chern Character, Boundaries and Index Formulæ

For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have ‘geometric K-theory’, namely the ‘transmission algebra’ introduced by Boutet de Monvel [5], the ‘zero algebra’ introduced by Mazzeo in [9, 10] and the ‘scattering algebra’ from [16] we give explicit formulæ for the Chern character of the index bundle in terms of the symbols (including norma...

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...

Transgression on Hyperkähler Manifolds and Generalized Higher Torsion Forms

Transgression of the characteristic classes taking values in the differential forms is a reach source of the interesting algebraic objects. The examples include Chern-Simons and Bott-Chern forms which are given by the transgression of the Chern character form. Chern-Simons forms are defined for a vector bundle over an arbitrary real manifold and are connected with the representation of combinat...