Homotopy of the exceptional Lie group G2

Abstract

Let G be one of the following compact simply connected Lie groups: SU(3), Sp(2), G2. In the first two cases there is a well known stable decomposition of G as Q ∨ Sd where d = dim G and Q is a certain subspace of G. For SU(3), Q is the stunted complex quasiprojective space Σ(ℂP2/ℂP1) which fits into a cofibration sequence S3→Q→S5 with stable attaching map η:S5 → S4 For Sp(2), Q is the quaternionic quasi-projective space ℍℚ1 and fits into a cofibration sequence S3→Q→S7 with stable attaching map 2ν:S7→S4 (Here η and ν are generators of respectively.)