Geodesic
2-Primary Exponent Bounds for Lie Groups of Low Rank
Canadian mathematical bulletin, Tome 47 (2004) no. 1, pp. 119-132

Voir la notice de l'article provenant de la source Cambridge University Press

Exponent information is proven about the Lie groups $SU(3),\,SU(4),\,Sp(2)$ , and ${{G}_{2}}$ by showing some power of the $H$ -space squaring map (on a suitably looped connected-cover) is null homotopic. The upper bounds obtained are $8,\,32,\,64$ , and ${{2}^{8}}$ respectively. This null homotopy is best possible for $SU(3)$ given the number of loops, off by at most one power of 2 for $SU(4)$ and $Sp(2)$ , and off by at most two powers of 2 for ${{G}_{2}}$ .
DOI : 10.4153/CMB-2004-013-x
Mots-clés : 55Q52, Lie group, exponent 
Theriault, Stephen D. 2-Primary Exponent Bounds for Lie Groups of Low Rank. Canadian mathematical bulletin, Tome 47 (2004) no. 1, pp. 119-132. doi: 10.4153/CMB-2004-013-x
@article{10_4153_CMB_2004_013_x,
     author = {Theriault, Stephen D.},
     title = {2-Primary {Exponent} {Bounds} for {Lie} {Groups} of {Low} {Rank}},
     journal = {Canadian mathematical bulletin},
     pages = {119--132},
     year = {2004},
     volume = {47},
     number = {1},
     doi = {10.4153/CMB-2004-013-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-013-x/}
}
TY  - JOUR
AU  - Theriault, Stephen D.
TI  - 2-Primary Exponent Bounds for Lie Groups of Low Rank
JO  - Canadian mathematical bulletin
PY  - 2004
SP  - 119
EP  - 132
VL  - 47
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-013-x/
DO  - 10.4153/CMB-2004-013-x
ID  - 10_4153_CMB_2004_013_x
ER  - 
%0 Journal Article
%A Theriault, Stephen D.
%T 2-Primary Exponent Bounds for Lie Groups of Low Rank
%J Canadian mathematical bulletin
%D 2004
%P 119-132
%V 47
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2004-013-x/
%R 10.4153/CMB-2004-013-x
%F 10_4153_CMB_2004_013_x

[C1] [C1] Cohen, F. R., A short course in some aspects of classical homotopy theory. Lecture Notes in Math. 1286, Springer-Verlag, 1987, 1–92. Google Scholar

[C2] [C2] Cohen, F. R., Applications of loop spaces to some problems in topology. London Math. Soc. Lecture Notes Series 139 (1989), 11–20. Google Scholar

[DM1] [DM1] Davis, D. M. and Mahowald, M., Three contributions to the homotopy theory of the exceptional Lie groups G and F . J. Math. Soc. Japan 43 (1991), 661–671. Google Scholar

[DM2] [DM2] Davis, D. M. and Mahowald, M., Some remarks on v-periodic homotopy groups. LondonMath. Soc. Lecture Notes Series 176 (1992), 55–72. Google Scholar

[M] [M] Mimura, M., The homotopy groups of Lie groups of low rank. J. Math. Kyoto Univ. 6 (1967), 131–176. Google Scholar

[MT] [MT] Mimura, M. and Toda, H., Homotopy groups of SU(3), SU(4), and Sp(2). J. Math. Kyoto Univ. 3 (1964), 217–250. Google Scholar

[N] [N] Neisendorfer, J. A., Properties of certain H-spaces. Quart. J. Math. Oxford 34 (1983), 201–209. Google Scholar

[R] [R] Richter, W., The H-space squaring map on Ω3S4n+1 factors through the double suspension. Proc. Amer.Math. Soc. 123 (1995), 3889–3900. Google Scholar

Cité par Sources :