Abstract
We present a fairly general construction of unbounded representatives for the interior Kasparov product. As a main tool we develop a theory of C1-connections on operator *-modules; we do not require any smoothness assumptions; our σ-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.
Original language | English |
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Journal | Advances in Mathematics |
Volume | 248 |
Pages (from-to) | 495-530 |
Number of pages | 36 |
ISSN | 0001-8708 |
DOIs | |
Publication status | Published - 25. Nov 2013 |
Externally published | Yes |
Keywords
- KK-theory
- Kasparov product
- Operator modules
- Primary
- Secondary
- Spectral flow