Norio Iwase

Mailing Adress: Faculty of Mathematics, Kyushu University, Motooka 744, Fukuoka 819-0395, Japan
E-mail Adress: iwase_AT__AT_math.kyushu-u.ac.jp

Japanese
Authors.
M. Mimura and myself
Abstract.
We determine the L-S category of Sp(3) by showing that the 5-fold reduced diagonal is given by ν2, using a Toda bracket and a generalised cohomology theory h* given by h*(X,A) = {X/A,S[0,2]}, where S[0,2] is the 3-stage Postnikov piece of the sphere spectrum S. This method also yields a general result that cat(Sp(n)) ≥ n+2 for n ≥ 3, which improves the result of Singhof.

L-S categories of simply-connected compact simple Lie groups of low rank (adobe-pdf file, 204805 bytes)