范畴序列
Categorical sequences
摘要：
我们定义并研究了空间的范畴序列，这是一种新的形式主义，它简化了空间X的Lusternik-Schnirelmann范畴的计算，通过在其CW范畴上的归纳。CW复形X的范畴序列中的第k项σ_X（k）是cat_X（X_n）>= k的最小整数n。我们证明了σ_X是X的一个定义良好的同伦不变量。证明了σ_X（k+l）>= σ_X（k）+ σ_X（l），这是判定范畴序列幂的三个关键之一。除了这个公式，我们提供的公式有关的范畴序列的空间和他们的一些代数不变式，包括他们的上同调代数和他们的理性模式，我们还发现之间的关系的范畴序列的空间中的纤维化序列，并给出一个初步结果的范畴序列的产品的两个空间在理性的情况下。我们完全刻画了可以作为形式理性空间的范畴序列出现的序列。我们提供的许多例子中最重要的是一个简单的证明吉安娜定理：如果X是李群Sp（3）的Mislin亏格的成员，那么cat（X）= cat（Sp（3））。
英文摘要：
We define and study the categorical sequence of a space, which is a new formalism that streamlines the computation of the Lusternik-Schnirelmann category of a space X by induction on its CW skeleta. The k-th term in the categorical sequence of a CW complex X, σ_X(k), is the least integer n for which cat_X(X_n) >= k. We show that σ_X is a well-defined homotopy invariant of X. We prove that σ_X(k+l) >= σ_X(k) + σ_X(l), which is one of three keys to the power of categorical sequences. In addition to this formula, we provide formulas relating the categorical sequences of spaces and some of their algebraic invariants, including their cohomology algebras and their rational models; we also find relations between the categorical sequences of the spaces in a fibration sequence and give a preliminary result on the categorical sequence of a product of two spaces in the rational case. We completely characterize the sequences which can arise as categorical sequences of formal rational spaces. The most important of the many examples that we offer is a simple proof of a theorem of Ghienne: if X is a member of the Mislin genus of the Lie group Sp(3), then cat(X) = cat(Sp(3)).
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