摘要

Let G be an exceptional Lie group G(2), F(4), E(6), E(7) or E(8), and also set p is the corresponding prime 7, 13, 13, 19 or 31 respectively. If we localize spaces at p, G can be decomposed into a product of spheres. Using this decomposition, we take some elements in the homotopy groups of p-localized G, and we offer some non-zero 3-fold Samelson products of them. This implies that the nilpotency class of the localized self-homotopy group of G is greater than or equal to 3.
The key lemma for these results is about a calculation on the cohomology operator P(1) in the mod p cohomology of BG, where G and p are as above. During this calculation, we use some original ideas, which are also used in Kishimoto and Kaji (in press) [7] recently.

  • 出版日期2010-2-1