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, T. Nishimoto and myself
Abstract.
Let X be the total space of a fibre bundle over a d-1 connected finite dimensional space B with fibre F whose structure group is a compact Lie group G, d ≥ 1. We prove the strong L-S category of X is less than or equal to m + dim B/d, if there are m cofibre sequences Ki -> Fi-1 -> Fi, (1 ≤ i ≤ m) with F0 = * and Fm homotopy equivalent to F with an additional assumption that the action G(d(i+2)-2)xFj -> F is compressible into Fi+j for all 0 ≤ i,j ≤ i+j ≤ m. Using it, we determine the L-S and strong L-S categories of SO(n) for n ≤ 9, PO(8) and PU(n) for n ≤ 5 by computing cup-length and category weight introduced by Rudyak and Strom. All of the above Lie groups satisfy the Ganea conjecture on L-S category.

Lusternik-Schnirelmann categories of non-simply connected compact simple Lie groups of low rank (adobe-pdf file, 134822 bytes)