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# NCG

## Seminar

### Relative pairing in cycle cohomology and divisor flows

Pflaum, M (John Wolfgang Goethe University)
Monday 31 July 2006, 15:30-16:30

Seminar Room 1, Newton Institute

#### Abstract

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.

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