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.
A. Kono and myself
Abstract.
Let G be a compact connected Lie group and (E,p,∑2V,G) a principal G-bundle with a characteristic map α on A=∑V to G. By combining cone decomposition arguments in I.-Mimura-Nishimoto on Spin(7) and I.-Mimura-Nishimoto on Lie groups of low rank with computations of higher Hopf invariants introduced in I., we further generalise the method of I.-Mimura: Let {Fi(G) &bar; 0 ≤ i ≤ m} be a cone-decomposition of G with a canonical structure map σi of cat(Fi) ≤ i for i ≤ m. We have cat(E) ≤ Max(m+n,m+2), if α is compressible into Fn(G) ⊆ Fm(G) ∼ G and Hnσn(α) = 0 for some n ≥ 1, under a suitable compatibility condition. On the other hand, calculations of Hamanaka-Kono and Ishitoya-Kono-Toda on spinor groups yields a lower estimate for the L-S category of spinor groups by means of a new computable invariant Mwgt(-;F2) which is stronger than wgt(-;F2) introduced by Rudyak and Strom. As a result, we obtain cat(Spin(9))=Mwgt(Spin(9);F2) = 8 > 6 = wgt(Spin(9);F2).

Lusternik-Schnirelmann categories of Spin(9) (adobe-pdf file, 180kbytes)