Spectral flow and the unbounded Kasparov product
  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. 
Jens Kaad and Matthias Lesch
math.OA math.DG math.FA