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Title:
Index Theorems for Weak Invariants
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Abstract:
The algebras of physical observables are usually represented on Hilbert spaces, which are linear spaces over the field of complex numbers endowed with a scalar product. But they can be also represented on Hilbert modules where the field of complex numbers is replaced by a generic algebra and this is at the heart of Kasparov's KK-theory. Paralleling the index theorems for the strong invariants derived within the ordinary K-theory [1], we show how generalized index theorems can be obtain for the weak invariants within Kasparov's KK-theory. The implications for the regime of strong disorder will be discussed.
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