Riemannian submersions and factorization of Dirac operators

Jens Kaad, Walter D. van Suijlekom

Research output: Contribution to journalJournal articleResearchpeer-review

71 Downloads (Pure)


We establish the factorization of Dirac operators on Riemannian submersions of compact spinc manifolds in unbounded KK-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 KKtheory. We show that our tensor sum represents the bounded KK-product of the corresponding KK-cycles and connect to the early work of Connes and Skandalis.

Original languageEnglish
JournalJournal of Noncommutative Geometry
Issue number3
Pages (from-to)1133-1159
Number of pages27
Publication statusPublished - 1. Jan 2018


  • Dirac operators
  • Riemannian submersions
  • Spin-c structures
  • Unbounded KK-theory
  • Wrong way functoriality.


Dive into the research topics of 'Riemannian submersions and factorization of Dirac operators'. Together they form a unique fingerprint.

Cite this