TWO SPECIAL CASES OF GANEA'S CONJECTURE
TWO SPECIAL CASES OF GANEA'S CONJECTURE
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GANEA 猜想的两个特殊情况
DOI：
10.1090/s0002-9947-99-02046-2
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发表时间：
1999
影响因子：
1.3
通讯作者：
J. Strom
中科院分区：
文献类型：
--
作者：
J. Strom
Ganea推测，对于任意有限CW复形X和任意k > 0, cat(X X Sk) cat(X) + 1。本文证明了这一猜想的两个特例。主要结果如下。设X是一个（p - 1）连通的n维CW复形（不一定有限）。我们证明了如果cat(X) K J +1和n $- 1 mod（这意味着p > 1），则cat(X Sk) cat(X) +1。通过在更大的范围内证明wcat(X X Sk) = wcat(X) + I，然后证明在施加的条件下，cat(X) = wcat(X)来证明这一点。第二个特例是Singhof之前关于流形的结论的扩展。
Ganea conjectured that for any finite CW complex X and any k > 0, cat(X X Sk) Cat(X) + 1. In this paper we prove two special cases of this conjecture. The main result is the folloNving. Let X be a (p - 1)- connected n-dimensional CW complex (not necessarily finite). We show that if cat(X) K J +1 and n $-l modp (which implies p > 1), then cat(X Sk) cat(X) + 1. This is proved by showing that wcat(X x Sk) = wcat(X) + I in a much larger range, and then showing that under the conditions imposed, cat(X) = wcat(X). The second special case is an extension of Singhof's earlier result for manifolds.