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arXiv · 1110.1472

Spectral flow and the unbounded Kasparov product

Jens Kaad·Matthias Lesch
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Abstract

We present a fairly general construction of unbounded representatives for the interior Kasparov product. As a main tool we develop a theory of C^1-connections on operator * modules; we do not require any smoothness assumptions; our sigma-unitality assumptions are minimal. Furthermore, we use work of Kucerovsky and our recent Local Global Principle for regular operators in Hilbert C*-modules. As an application we show that the Spectral Flow Theorem and more generally the index theory of Dirac-Schrödinger operators can be nicely explained in terms of the interior Kasparov product.

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BibTeXRIS

Jens Kaad, Matthias Lesch. 2011-10-07. Spectral flow and the unbounded Kasparov product. https://doi.org/10.1016/j.aim.2013.08.015

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