Co-H-spaces and the Ganea conjecture
Co-H-spaces and the Ganea conjecture
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Co-H-空间和 Ganea 猜想
DOI：
10.1016/s0040-9383(99)00052-x
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
Norio Iwase
中科院分区：
文献类型：
--
作者：
Norio Iwase
非单连通共 H 空间 X 是同伦之前的纤维单连通指向纤维共霍普夫纤维 j 的总空间： X→Bπ1(X) ，这是沿 j 具有 Bπ1(X) 共同作用的空间。我们构建了它的同源分解，这产生了它的纤维定位的简单结构。我们的主要结果是构造了一系列共H空间，每个空间都不能分解为一个简单连通空间和一堆圆的一点和，从而反驳了Ganea猜想。
A non-simply connected co-H-space X is, up to homotopy, the total space of a fibrewise-simply connected pointed fibrewise co-Hopf fibrant j : X→Bπ1(X) , which is a space with a co-action of Bπ1(X) along j. We construct its homology decomposition, which yields a simple construction of its fibrewise localisation. Our main result is the construction of a series of co-H-spaces, each of which cannot be split into a one-point-sum of a simply connected space and a bunch of circles, thus disproving the Ganea conjecture.