On the homotopy type of positively-pinched manifolds
On the homotopy type of positively-pinched manifolds
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关于正收缩流形的同伦型
DOI：
10.1007/bf01899493
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发表时间：
1967
影响因子：
0.6
通讯作者：
A. Weinstein
中科院分区：
文献类型：
--
作者：
A. Weinstein
2.估计数值不变量。推论表明，任何数值同伦不变量是有界的，当限制到2n维，6-捏流形。B~ RGErr [1]和Bm~ OER-BOTT [2]给出了两个不变量的数值上界，即欧拉特征线的绝对值和循环空间Betti数的累积和。我们的定理产生的Bctti数的流形本身的估计。当这些估计相加时，产生不如B~ oER的IZI估计。一个谱序列的参数导致了对循环空间的贝蒂数的累积和的估计;同样，BERr的估计更好，并且它们也适用于奇数维。
2. Estimating numerical invariants. The Corollary shows that any numerical homotopy invariant is bounded when restricted to 2n-dimensional, 6-pinched manifolds. B~ RGErr [1] and Bm~ OER-BOTT [2] have obtained numerical upper bounds for two invariants, the absolute value of the Euler characteristic and the cumulative sums of Betti numbers of the loop space. Our Theorem yields estimates on the Bctti numbers of the manifold itself. These estimates, when added, yield an estimate for IZI which is not as good as B~ oER's. A spectral sequence argument leads to estimates for the cumulative sums of Betti numbers of the loop space; again, the estimates of BERr are better, and they work in odd dimensions as well.