Algebraic & Geometric Topology

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

Anssi Lahtinen

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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.

Article information

Source
Algebr. Geom. Topol., Volume 12, Number 4 (2012), 1925-1940.

Dates
Received: 9 March 2011
Revised: 4 May 2012
Accepted: 21 May 2012
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715444

Digital Object Identifier
doi:10.2140/agt.2012.12.1925

Mathematical Reviews number (MathSciNet)
MR2994825

Zentralblatt MATH identifier
1260.55008

Subjects
Primary: 55N15: $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19- XX}
Secondary: 19L50: Twisted $K$-theory; differential $K$-theory 19L47: Equivariant $K$-theory [See also 55N91, 55P91, 55Q91, 55R91, 55S91] 55P91: Equivariant homotopy theory [See also 19L47]

Keywords
completion twisted $K$–theory equivariant $K$–theory

Citation

Lahtinen, Anssi. The Atiyah–Segal completion theorem in twisted $K$–theory. Algebr. Geom. Topol. 12 (2012), no. 4, 1925--1940. doi:10.2140/agt.2012.12.1925. https://projecteuclid.org/euclid.agt/1513715444


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References

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