$2$-Primary Exponent Bounds for Lie Groups of Low Rank

[摘要] Exponent information is proven about the Lie groups $SU(3)$,$SU(4)$, $Sp(2)$, and $G_2$ by showing some power of the $H$-spacesquaring 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 ofloops, off by at most one power of~$2$ for $SU(4)$ and $Sp(2)$, andoff by at most two powers of $2$ for $G_2$.

[学科分类] 数学（综合）

[关键词] Lie group;exponent