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