The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Journal of Noncommutative Geometry


Full-Text PDF (466 KB) | Metadata | Table of Contents | JNCG summary
Volume 12, Issue 2, 2018, pp. 779–821
DOI: 10.4171/JNCG/291

Published online: 2018-07-02

A categorical perspective on the Atiyah–Segal completion theorem in KK-theory

Yuki Arano[1] and Yosuke Kubota[2]

(1) The University of Tokyo, Japan
(2) The University of Tokyo, Japan

We investigate the homological ideal $\mathcal J _G^H$, 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 $\mathcal J_G^H$ 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.

Keywords: Atiyah–Segal completion theorem, KK-theory, relative homological algebra

Arano Yuki, Kubota Yosuke: A categorical perspective on the Atiyah–Segal completion theorem in KK-theory. J. Noncommut. Geom. 12 (2018), 779-821. doi: 10.4171/JNCG/291