A-method in Lusternik-Schnirelmann category

研究成果: ジャーナルへの寄稿記事

17 引用 (Scopus)

抄録

To clarify the method behind (Iwase, Bull. Lond. Math. Soc. 30 (1998), 623-634), a generalisation of Berstein-Hilton Hopf invariants is defined as 'higher Hopf invariants'. They detect the higher homotopy associativity of Hopf spaces and are studied as obstructions not to increase the LS category by one by attaching a cone. Under a condition between dimension and LS category, a criterion for Ganea's conjecture on LS category is obtained using the generalised higher Hopf invariants, which yields the main result of (Iwase, Bull. Lond. Math. Soc. 30 (1998), 623-634) for all the cases except the case when p = 2. As an application, conditions in terms of homotopy invariants of the characteristic maps are given to determine the LS category of sphere-bundles-over-spheres. Consequently, a closed manifold M is found not to satisfy Ganea's conjecture on LS category and another closed manifold N is found to have the same LS category as its 'punctured submanifold' N - {P}, P ε N. But all examples obtained here support the conjecture in (Iwase, Bull. Lond. Math. Soc. 30 (1998), 623-634).

元の言語英語
ページ(範囲)695-723
ページ数29
ジャーナルTopology
41
発行部数4
DOI
出版物ステータス出版済み - 4 3 2002

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Lusternik-Schnirelmann Category
Hopf Invariant
Homotopy
Closed
Associativity
Obstruction
Submanifolds
Bundle
Cone
Invariant

All Science Journal Classification (ASJC) codes

  • Geometry and Topology

これを引用

A-method in Lusternik-Schnirelmann category. / Iwase, Norio.

:: Topology, 巻 41, 番号 4, 03.04.2002, p. 695-723.

研究成果: ジャーナルへの寄稿記事

Iwase, Norio. / A-method in Lusternik-Schnirelmann category. :: Topology. 2002 ; 巻 41, 番号 4. pp. 695-723.
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