A categorical perspective on the Atiyah–Segal completion theorem in KK-theory
Yuki Arano
The University of Tokyo, JapanYosuke Kubota
The University of Tokyo, Japan
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Abstract
We investigate the homological ideal , the kernel of the restriction functors in compact Lie group equivariant Kasparov categories. Applying the relative homological algebra developed by Meyer and Nest, we relate the Atiyah–Segal completion theorem with the comparison of with the augmentation ideal of the representation ring.
In relation to it, we study on the Atiyah–Segal completion theorem for groupoid equivariant KK-theory, McClure's restriction map theorem and permanence property of the Baum–Connes conjecture under extensions of groups.
Cite this article
Yuki Arano, Yosuke Kubota, A categorical perspective on the Atiyah–Segal completion theorem in KK-theory. J. Noncommut. Geom. 12 (2018), no. 2, pp. 779–821
DOI 10.4171/JNCG/291