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Buggisch, Lukas Werner: The spectral flow theorem for families of twisted Dirac operators. 2018
Inhalt
C*-algebras, Hilbert modules and KK-Theory
C*-algebras
Hilbert modules
Bounded operators on Hilbert modules
Unbounded operators on Hilbert modules
Tensor products of Hilbert modules
KK-Theory
Functoriality
The Kasparov product
Unbounded Kasparov modules
Clifford algebras and Periodicity
KK-equivalence and Bott isomorphism
Bundles and operators
Bundles of Hilbert Modules
Connections
KO-theory of A-bundles
A-linear differential operators
Differential operators as unbounded A-linear operators
Families of A-linear operators
Continuous fields
Continuous Fields
Application
Extension by zero
Two Versions of the Index Difference
Preliminaries
The Index Difference
Hitchin's Version
Gromov and Lawson's Version
The spectral flow theorem for families of twisted Dirac operators
An approximation of `39`42`"613A``45`47`"603AinddiffGL
Calculation of the Kasparov product
Bibliography