Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory

Deformation quantization and the Baum-Connes conjecture

Alternative titles of this paper would have been `Index theory without index' or `The Baum-Connes conjecture without Baum.' In 1989, Rieffel introduced an analytic version of deformation quantization based on the use of continuous fields of C*-algebras. We review how a wide variety of examples of such quantizations can be understood on the basis of a single lemma involving amenable groupoids. These include Weyl-Moyal quantization on manifolds, C*-algebras of Lie groups and Lie groupoids, and the E-theoretic version of the Baum-Connes conjecture for smooth groupoids as described by Connes in hi…

某些相对膨胀图的粗Baum-Connes猜想

The coarse Baum-Connes conjecture for certain relative expanders

本文证明了若有限群正合列序列中核与商群的粗不相交并可粗嵌入Hilbert空间，则原群的粗不相交并满足粗Baum-Connes猜想，由此解决了相对膨胀图相关的公开问题。

Twisted crystallograpic T-duality via the Baum--Connes isomorphism

We establish the twisted crystallographic T-duality, which is an isomorphism between Freed-Moore twisted equivariant K-groups of the position and momentum tori associated to an extension of a crystallographic group. The proof is given by identifying the map with the Dirac homomorphism in twisted Chabert--Echterhoff KK-theory. We also illustrate how to exploit it in K-theory computations.