The INI has a new website!

This is a legacy webpage. Please visit the new site to ensure you are seeing up to date information.

An Isaac Newton Institute Workshop

Noncommutative Geometry and Cyclic Cohomology

Relative pairing in cyclic cohomology and divisor flows

Author: Markus Pflaum (Johann Wolfgang Goethe University)


In the talk I elaborate on joint work with H. Moscovici and M. Lesch. We show that Melrose's divisor flow and its generalizations by Lesch and Pflaum are invariants of K-theory classes for algebras of parametric pseudodifferential operators on a closed manifold, obtained by pairing the relative K-theory modulo the symbols with the cyclic cohomological character of a relative cycle constructed out of the regularized operator trace together with its symbolic boundary. This representation gives a clear and conceptual explanation to all the essential features of the divisor flow -- its homotopy nature, additivity and integrality. It also provides a cohomological formula for the spectral flow along a smooth path of self-adjoint elliptic first order differential operators, between any two invertible such operators on a closed manifold.