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).
|Number of pages||13|
|Journal||Canadian Mathematical Bulletin|
|Publication status||Published - 2004|