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 language | English |
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Journal | Journal of Noncommutative Geometry |
Volume | 12 |
Issue number | 3 |
Pages (from-to) | 1133-1159 |
Number of pages | 27 |
ISSN | 1661-6952 |
DOIs | |
Publication status | Published - 1. Jan 2018 |
Keywords
- Dirac operators
- Riemannian submersions
- Spin-c structures
- Unbounded KK-theory
- Wrong way functoriality.