Spectral flow and the unbounded Kasparov product

Details Spectral flow and the unbounded Kasparov product Spectral flow and the unbounded Kasparov product

2011-10-07

arxiv.org/abs/1110.1472v1

Mathematics

Operator Algebras

40 pages

Scientific paper

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-Schr\"odinger operators can be nicely explained in terms of the interior Kasparov product.

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