The Atiyah–Segal completion theorem in twisted K–theory
Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 1925-1940
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

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.

DOI : 10.2140/agt.2012.12.1925
Keywords: completion, twisted $K$–theory, equivariant $K$–theory

Lahtinen, Anssi  1

1 Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen Ø, Denmark
@article{10_2140_agt_2012_12_1925,
     author = {Lahtinen, Anssi},
     title = {The {Atiyah{\textendash}Segal} completion theorem in twisted {K{\textendash}theory}},
     journal = {Algebraic and Geometric Topology},
     pages = {1925--1940},
     year = {2012},
     volume = {12},
     number = {4},
     doi = {10.2140/agt.2012.12.1925},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.1925/}
}
TY  - JOUR
AU  - Lahtinen, Anssi
TI  - The Atiyah–Segal completion theorem in twisted K–theory
JO  - Algebraic and Geometric Topology
PY  - 2012
SP  - 1925
EP  - 1940
VL  - 12
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.1925/
DO  - 10.2140/agt.2012.12.1925
ID  - 10_2140_agt_2012_12_1925
ER  - 
%0 Journal Article
%A Lahtinen, Anssi
%T The Atiyah–Segal completion theorem in twisted K–theory
%J Algebraic and Geometric Topology
%D 2012
%P 1925-1940
%V 12
%N 4
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2012.12.1925/
%R 10.2140/agt.2012.12.1925
%F 10_2140_agt_2012_12_1925
Lahtinen, Anssi. The Atiyah–Segal completion theorem in twisted K–theory. Algebraic and Geometric Topology, Tome 12 (2012) no. 4, pp. 1925-1940. doi: 10.2140/agt.2012.12.1925

[1] J F Adams, J P Haeberly, S Jackowski, J P May, A generalization of the Atiyah–Segal completion theorem, Topology 27 (1988) 1

[2] J F Adams, J P Haeberly, S Jackowski, J P May, A generalization of the Segal conjecture, Topology 27 (1988) 7

[3] M F Atiyah, G B Segal, Equivariant K–theory and completion, J. Differential Geometry 3 (1969) 1

[4] M F Atiyah, G B Segal, Twisted K–theory, Ukr. Mat. Visn. 1 (2004) 287

[5] G Carlsson, Equivariant stable homotopy and Segal’s Burnside ring conjecture, Ann. of Math. 120 (1984) 189

[6] C Dwyer, Twisted K–theory and completion, to appear

[7] D S Freed, M J Hopkins, C Teleman, Twisted equivariant K–theory with complex coefficients, J. Topol. 1 (2008) 16

[8] D S Freed, M J Hopkins, C Teleman, Loop groups and twisted K–theory I, J. Topol. 4 (2011) 737

[9] G B Segal, The representation ring of a compact Lie group, Inst. Hautes Études Sci. Publ. Math. (1968) 113

Cité par Sources :