Comments on: "Operator $K$-theory for the group SU(n,1)" by P. Julg and G. Kasparov

Morita invariance of unbounded bivariant K-theory

We introduce a notion of Morita equivalence for non-selfadjoint operator algebras equipped with a completely isometric involution (operator *-algebras). We then show that the unbounded Kasparov product by a Morita equivalence bimodule induces an isomorphism between equivalence classes of twisted spectral triples over Morita equivalent operator *-algebras. This leads to a tentative definition of unbounded bivariant K-theory and we prove that this bivariant theory is related to Kasparov's bivariant K-theory via the Baaj-Julg bounded transform. Moreover, the unbounded Kasparov product provides a …

On the Baum-Connes Conjecture for Groups Acting on CAT(0)-Cubical Spaces

We give a new proof of the Baum--Connes conjecture with coefficients for any second countable, locally compact topological group that acts properly and cocompactly on a finite-dimensional CAT(0)-cubical space with bounded geometry. The proof uses the Julg-Valette complex of a CAT(0)-cubical space introduced by the first three authors, and the direct splitting method in Kasparov theory developed by the last author.

KK-理论中的谱局部化子

Spectral localizers in KK-theory

本文研究偶KK-理论中由Kasparov积导出的偶K-群指标同态，利用无界Kasparov模块和谱局部化子给出了不依赖完整谱的显式公式，并推广了Loring和Schulz-Baldes的指标配对工作。