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arXiv · 1610.02873

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 spin$^c$ 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.

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Jens Kaad, Walter D. van Suijlekom. 2016-10-10. Riemannian submersions and factorization of Dirac operators. https://arxiv.org/abs/1610.02873

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