Abstract
Let p be an odd prime. Using homotopy decompositions and spherical fibrations, under certain dimensional restrictions, we obtain upper bounds of the p-primary homotopy exponents of some homogeneous spaces such as generalized complex Stiefel manifolds, generalized complex Grassmann manifolds, SU (2n)/Sp (n), E6/F4 and F4/G2 (the latter for p = 2 and p ? 5).
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