岩 瀬　則 夫 （いわせ　のりお）

郵便宛て先：〒８１９-０３９５ 福岡市 西区 元岡７４４ 九州大学 数理学研究院
電子メール：iwase_AT_math.kyushu-u.ac.jp

English
Authors.
myself, Kai Kikuchi and Toshiyuki Miyauchi
Journal.
Fundamenta Mathematicae 234 (2016), 201-227.
Abstract.
Let G be a compact connected Lie group and p : E → ΣA be a principal G-bundle with a characteristic map α : A → G, where A = ΣA0 for some A0. Let {Ki→Fi-1→Fi | 1 ≤ i ≤ m} with F0={*}, F1=ΣK1 and Fm≅G be a cone-decomposition of G of length m and F′1 = ΣK′1 ⊂ F1 with K'1 ⊂ K1 which satisfy FiF′1 ⊂ Fi+1 upto homotopy for all i. Then we have cat(E) ≤ m+1, under some suitable conditions, which is used to determine cat(SO(10)). A similar result is obtained by Kono and the first author [9] to determine cat(Spin(9)), while the result in [9] can not assert cat(E) ≤ m+1.

Ganea's conjecture on LS-category (adobe-pdf file, 806 Kbytes)