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
Authors.
myself
Journal.
Topology, to appear.
Abstract.
Berstein-Hilton Hopf invariants are generalised to detect the higher homotopy associativity of a Hopf space as `higher Hopf invariants', which are studied as obstructions for normalised Lusternik-Schnirelmann category, LS category for short.
Under a condition among dimension and LS category, the criterion for Ganea's conjecture on LS category is obtained using the stabilised higher Hopf invariants and the conjecture in "Ganea's conjecture on Lusternik-Schnirelmann category" is verified, which yields the main result in it except the case when p=2.
As an application, conditions in terms of homotopy invariants of the attaching maps are given to determine LS category of sphere-bundles-over-spheres:
A closed manifold is found to have the same LS category as its punctured submanifold and another closed manifold is found not to satisfy Ganea's conjecture on LS category.
- A∞-method in LS-category (adobe-pdf file, 238071 bytes)