Spectral flow and the unbounded Kasparov product

Jens Kaad, Matthias Lesch

Research output: Contribution to journalJournal articleResearchpeer-review

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 languageEnglish
JournalAdvances in Mathematics
Volume248
Pages (from-to)495-530
Number of pages36
ISSN0001-8708
DOIs
Publication statusPublished - 25. Nov 2013
Externally publishedYes

Keywords

  • KK-theory
  • Kasparov product
  • Operator modules
  • Primary
  • Secondary
  • Spectral flow

Fingerprint

Dive into the research topics of 'Spectral flow and the unbounded Kasparov product'. Together they form a unique fingerprint.

Cite this