Riemannian submersions and factorization of Dirac operators
K-Theory and Homology
2016-10-11 v1 Differential Geometry
Abstract
We establish the factorization of Dirac operators on Riemannian submersions of compact spin 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 KK-theory. 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.
Keywords
Cite
@article{arxiv.1610.02873,
title = {Riemannian submersions and factorization of Dirac operators},
author = {Jens Kaad and Walter D. van Suijlekom},
journal= {arXiv preprint arXiv:1610.02873},
year = {2016}
}
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26 pages