Riemannian submersions and factorization of Dirac operators

Jens Kaad, Walter D. van Suijlekom

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Abstract

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
Volume12
Issue number3
Pages (from-to)1133-1159
Number of pages27
ISSN1661-6952
DOIs
Publication statusPublished - 1. Jan 2018

Keywords

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

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