11 citations · 15 across the 6 of their papers we have counts for
8 papers
Spectral Triples and Generalized Crossed Products
Olivier Gabriel, Martin Grensing
We give a construction allowing to lift spectral triples to crossed products by Hilbert bimodules. The spectral triple one obtains is a concrete unbounded representative of the Kas…
Ergodic Actions and Spectral Triples
Olivier Gabriel, Martin Grensing
In this article, we give a general construction of spectral triples from certain Lie group actions on unital C*-algebras. If the group G is compact and the action is ergodic, we ac…
Noncommutative stable homotopy theory
Martin Grensing
We construct Kasparov's bifunctor and -theory by stable homotopy theoretic methods. This is motivated by results concerning constructions of bivariant theories on more gene…
Six-Term Exact Sequences for Smooth Generalized Crossed Products
Olivier Gabriel, Martin Grensing
We define smooth generalized crossed products and prove six-term exact sequences of Pimsner-Voiculescu type. This sequence may, in particular, be applied to smooth subalgebras of t…
The Thom isomorphism in bivariant K-theory
Martin Grensing
We give a simple proof of the smooth Thom isomorphism for complex bundles for the bivariant K-theories on locally convex algebras considered by Cuntz. We also prove the Thom isomor…
A note on Kasparov products
Martin Grensing
Combining Kasparov's theorem of Voiculesu and Cuntz's description of -theory in terms of quasihomomorphisms, we give a simple construction of the Kasparov product. This will be…