Geodesic
Classifying spaces of twisted loop groups
Baird, Thomas J1
1Department of Mathematics & Statistics, Memorial University of Newfoundland, St. John’s NF A1C 5S7, Canada
Algebraic and Geometric Topology, Tome 16 (2016) no. 1, pp. 211-229
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

We study the classifying space of a twisted loop group LσG, where G is a compact Lie group and σ is an automorphism of G of finite order modulo inner automorphisms. Equivalently, we study the σ–twisted adjoint action of G on itself. We derive a formula for the cohomology ring H∗(BLσG) and explicitly carry out the calculation for all automorphisms of simple Lie groups. More generally, we derive a formula for the equivariant cohomology of compact Lie group actions with constant rank stabilizers.

DOI : 10.2140/agt.2016.16.211
Classification : 22E67, 57S15
Keywords: loop groups, twisted conjugacy, twisted adjoint action, equivariant cohomology, classifying spaces, gauge groups

Baird, Thomas J  1

1 Department of Mathematics & Statistics, Memorial University of Newfoundland, St. John’s NF A1C 5S7, Canada 
@article{10_2140_agt_2016_16_211,
     author = {Baird, Thomas J},
     title = {Classifying spaces of twisted loop groups},
     journal = {Algebraic and Geometric Topology},
     pages = {211--229},
     year = {2016},
     volume = {16},
     number = {1},
     doi = {10.2140/agt.2016.16.211},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.211/}
}
TY  - JOUR
AU  - Baird, Thomas J
TI  - Classifying spaces of twisted loop groups
JO  - Algebraic and Geometric Topology
PY  - 2016
SP  - 211
EP  - 229
VL  - 16
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.211/
DO  - 10.2140/agt.2016.16.211
ID  - 10_2140_agt_2016_16_211
ER  - 
%0 Journal Article
%A Baird, Thomas J
%T Classifying spaces of twisted loop groups
%J Algebraic and Geometric Topology
%D 2016
%P 211-229
%V 16
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2016.16.211/
%R 10.2140/agt.2016.16.211
%F 10_2140_agt_2016_16_211
Baird, Thomas J. Classifying spaces of twisted loop groups. Algebraic and Geometric Topology, Tome 16 (2016) no. 1, pp. 211-229. doi: 10.2140/agt.2016.16.211

[1] J C Baez, The octonions, Bull. Amer. Math. Soc. 39 (2002) 145

[2] T J Baird, Cohomology of the space of commuting n–tuples in a compact Lie group, Algebr. Geom. Topol. 7 (2007) 737

[3] T Baird, Moduli spaces of vector bundles over a real curve : Z∕2–Betti numbers, Canad. J. Math. 66 (2014) 961

[4] A Borel, Topology of Lie groups and characteristic classes, Bull. Amer. Math. Soc. 61 (1955) 397

[5] A M Gleason, Spaces with a compact Lie group of transformations, Proc. Amer. Math. Soc. 1 (1950) 35

[6] K Kuribayashi, M Mimura, T Nishimoto, Twisted tensor products related to the cohomology of the classifying spaces of loop groups, 849, Amer. Math. Soc. (2006)

[7] S Mohrdieck, R Wendt, Integral conjugacy classes of compact Lie groups, Manuscripta Math. 113 (2004) 531

[8] R S Palais, Foundations of global non-linear analysis, W A Benjamin (1968)

[9] A Pressley, G Segal, Loop groups, , Oxford Univ. Press (1986)

[10] G Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. (1968) 105

[11] J De Siebenthal, Sur les groupes de Lie compacts non connexes, Comment. Math. Helv. 31 (1956) 41

[12] S Stanciu, A geometric approach to D–branes in group manifolds, Fortschr. Phys. 50 (2002) 980

[13] R Wendt, Weyl’s character formula for non-connected Lie groups and orbital theory for twisted affine Lie algebras, J. Funct. Anal. 180 (2001) 31

Cité par Sources :