Connes-Chern character in relative K-homology
نویسندگان
چکیده
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-character will be introduced in this abstract setting. Lecture 2 (Pflaum): An introduction to the b-calculus and the b-trace The b-calculus has been invented by R. Melrose as a framework for index theory over manifolds with boundary or more general spaces with singularities. The b-trace is a crucial tool to prove the index theorem by Atiyah-Singer-Patodi in this framework. The talk will provide an introduction in this area. Lecture 3 (Pflaum): The Connes-Chern character in various relative geometric-analytic situations In this talk it is explained how regularizations such as the b-trace or regularized traces on parametric pseudodifferential operators give rise to relative Chern characters and corresponding pairings in relative cyclic cohomology. Moreover, it is shown how this noncommutative geometric approach helps to clarify and conceptually explain the essential features of the invariants obtained by relative pairings in relative cyclic cohomology. Lecture 4 (Lesch): Transgression of the Connes-Chern a la Connes-Moscovici Rougly speaking the Connes-Chern character is a natural transformation from K-homology to cyclic cohomology which generalizes the classical geometric Chern character. However, cyclic cohomology comes in various flavors and so does the Chern character. The JLO cocycle, which from the point of view of local index theory is very nat-
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