A∞-method in Lusternik–Schnirelmann category
A∞-method in Lusternik–Schnirelmann category
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Lusternik-Schnirelmann 范畴中的 A∞-方法
DOI：
10.1016/s0040-9383(00)00045-8
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
Norio Iwase
中科院分区：
文献类型：
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作者：
Norio Iwase
澄清背后的方法(Iwase, Bull。Lond。数学。Soc. 30(1998), 623-634)，将Berstein-Hilton Hopf不变量的推广定义为“更高的Hopf不变量”。它们检测了Hopf空间的高同伦结合性，并作为不通过附加一个锥使LS类别增加一个的障碍进行了研究。在维数与LS范畴之间的条件下，利用广义高Hopf不变量，得到了LS范畴上Ganea猜想的判据，得到了（Iwase, Bull）的主要结果。Lond。数学。Soc. 30(1998), 623-634)适用于除p=2的情况外的所有情况。作为应用，给出了利用特征映射的同伦不变量来确定球-球束-球上的LS范畴的条件。因此，我们发现一个闭流形M不满足Ganea关于LS范畴的猜想，并且发现另一个闭流形N与其“被刺穿的子流形”N−{P}， P∈N具有相同的LS范畴。但是这里得到的所有例子都支持Iwase， Bull的猜想。Lond。数学。社会法学，30(1998),623-634)。
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∈N . But all examples obtained here support the conjecture in (Iwase, Bull. Lond. Math. Soc. 30 (1998), 623–634).