2-Primary Exponent Bounds for Lie Groups of Low Rank

Abstract

AbstractExponent information is proven about the Lie groups SU(3), SU(4), Sp(2), and G2 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 28 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 G2.