Volume 12, issue 4 (2012)

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The Atiyah–Segal completion theorem in twisted $K$–theory

Anssi Lahtinen

Algebraic & Geometric Topology 12 (2012) 1925–1940
Abstract

A basic result in equivariant $K$–theory, the Atiyah–Segal completion theorem relates the $G$–equivariant $K$–theory of a finite $G$–CW complex to the non-equivariant $K$–theory of its Borel construction. We prove the analogous result for twisted equivariant $K$–theory.

Keywords
completion, twisted $K$–theory, equivariant $K$–theory
Mathematical Subject Classification 2000
Primary: 55N15
Secondary: 19L50, 19L47, 55P91