Spectral flow and the unbounded Kasparov product
80 citations recorded by the source corpus.
Abstract 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 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–Schrodinger operators can be nicely explained in terms of the interior Kasparov product.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/cad2e0af121a07d636b73ee40326518a953cc4e5
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Nonunital spectral triples and metric completeness in unbounded KK-theory (2015, methodology): “This is done by associating to a bounded Kasparov module a correspondence in a slightly broader sense than was used in [13, 31, 41].”