Relative pairing in cyclic cohomology and divisor flows Journal Article uri icon

Overview

abstract

  • AbstractWe construct invariants of relative K-theory classes of multiparameter dependent pseudodifferential operators, which recover and generalize Melrose's divisor flow and its higher odd-dimensional versions of Lesch and Pflaum. These higher divisor flows are obtained by means of pairing the relative K-theory modulo the symbols with the cyclic cohomological characters of relative cycles constructed out of the regularized operator trace together with its symbolic boundary. Besides giving a clear and conceptual explanation to the essential features of the divisor flows, namely homotopy invariance, additivity and integrality, this construction allows to uncover the previously unknown even-dimensional counterparts. Furthermore, it confers to the totality of these invariants a purely topological interpretation, that of implementing the classical Bott periodicity isomorphisms in a manner compatible with the suspension isomorphisms in both K-theory and in cyclic cohomology. We also give a precise formulation, in terms of a natural Clifford algebraic suspension, for the relationship between the higher divisor flows and the spectral flow.

publication date

  • April 1, 2009

Full Author List

  • Lesch M; Moscovici H; Pflaum MJ

Other Profiles

Additional Document Info

start page

  • 359

end page

  • 407

volume

  • 3

issue

  • 2