Riemannian submersions and factorization of Dirac operators

  • Jens Kaad

    Syddansk Universitet, Odense, Denmark
  • Walter D. van Suijlekom

    Radboud University Nijmegen, Netherlands

Abstract

We establish the factorization of Dirac operators on Riemannian submersions of compact spin manifolds in unbounded -theory. More precisely, we show that the Dirac operator on the total space of such a submersion is unitarily equivalent to the tensor sum of a family of Dirac operators with the Dirac operator on the base space, up to an explicit bounded curvature term. Thus, the latter is an obstruction to having a factorization in unbounded -theory. We show that our tensor sum represents the bounded KK-product of the corresponding -cycles and connect to the early work of Connes and Skandalis.

Cite this article

Jens Kaad, Walter D. van Suijlekom, Riemannian submersions and factorization of Dirac operators. J. Noncommut. Geom. 12 (2018), no. 3, pp. 1133–1159

DOI 10.4171/JNCG/299