Category weight: new ideas concerning Lusternik-Schnirelmann category
Category weight: new ideas concerning Lusternik-Schnirelmann category
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类别权重：关于 Lusternik-Schnirelmann 类别的新想法
DOI：
10.4064/-45-1-47-61
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发表时间：
1998
期刊：
影响因子：
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通讯作者：
Yuli B. Rudyak
中科院分区：
文献类型：
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作者：
Yuli B. Rudyak
导言。范畴权重的概念是由Fadell-Husseini[FH]引入的，由Rudyak和Strom发展起来的。本文对范畴权重进行了综述，并对范畴权重的进一步发展和应用进行了展望。拓扑空间X的Lusternik-Schnirelmann范畴CATx被定义为使得X有可数覆盖{A1，.。。Lusternik和Schnirelmann[LS]引入了流形的不变CATx。证明了对每个连通光滑(=C∞)闭流形M，1+CATM≤CritM：=Min{Crit f|f∈C∞(M，R)}
Introduction. The concept of category weight was introduced by Fadell–Husseini [FH] and developed by Rudyak and Strom. Here we give a survey, some further development and applications of category weight. The Lusternik–Schnirelmann category of a topological space X, catX, is defined as the minimal number k such that X admits a numerable covering {A1, . . . , Ak+1} where each Ai is contractible in X. Lusternik and Schnirelmann [LS] introduced the invariant catX for manifolds. They proved that, for every connected smooth (=C∞) closed manifold M , 1 + catM ≤ CritM := min{crit f |f ∈ C∞(M,R)}