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Classification of the cohomology rings of finite Hopf spaces

有限Hopf空间上同调环的分类

基本信息

批准号：
11640083
负责人：
HEMMI Yutaka
金额：
$ 2.24万
依托单位：
KOCHI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640083/
关键词：
Hopf spaces iterated H-deviation Steenrod operations higher order operations quasi p-regular homotopy groups of spheres self homotopy equivalences Moore space mod p cohomology Moore space 同変ホモトピー

项目摘要

The summary of reserch results is as follows.1. We constructed p-th order mod p unstable cohomology operations for any odd prime p. Then, by using the operation, we studied the action of the Steenrod operations on the cohomology of the mod p finite Hopf spaces. We gave a lecture on a part of our resutl at the Japan-America Mathematics Institute at the Johns Hopkins University held at March 2000.2. In order to apply the above p-th order operation to the cohomology of Hopf spaces, we introduced iterated H-deviation for maps between Hopf spaces, which is an extension of the H-deviation.3. We studied conditions for mod p finite Hopf spaces to be quase p-regular. Our result is a considered as a generalization of the result by Kumpel for the p-regularity of mod p finite Hopf spaces. Our result includes the results by Harper, McClearly and Wilkerson.4. O^^-shima determined the group structure of the set of self homotopy equivalences for the exceptional group G_2. While Morisugi determined the one for the classical groups SU (3), Sp (2).5. Shimomura studied the υ^<-1>_2BP-localized homotopy groups of the spheres localized at prime 2 or 3. Komatsu studied orbit closure decompositions of tiling spaces by the generalized projection method. Tsukiyama studied the group of homotopy equivalence classes of S^1-bundles.

研究结果总结如下： 1．我们为任何奇素数 p 构造了 p 阶 mod p 不稳定上同调运算。然后，利用该运算，研究了Steenrod运算对mod p有限Hopf空间上同调的作用。 2000年3月2日，我们在约翰·霍普金斯大学日美数学研究所举办的讲座中，对我们的部分结果进行了演讲。为了将上述p阶运算应用到Hopf空间的上同调中，我们引入了Hopf空间之间映射的迭代H偏差，它是H偏差的扩展。 3．我们研究了 mod p 有限 Hopf 空间拟 p-正则的条件。我们的结果被认为是 Kumpel 对 mod p 有限 Hopf 空间的 p 正则性结果的推广。我们的结果包括 Harper、McClearly 和 Wilkerson 的结果。4。 O^^-shima 确定了例外群 G_2 的自同伦等价集的群结构。而森杉则确定了经典群SU(3)、Sp(2).5。 Shimomura 研究了局域于素数 2 或 3 的球体的 υ^<-1>_2BP 局域同伦群。Komatsu 通过广义投影方法研究了平铺空间的轨道闭合分解。 Tsukiyama 研究了 S^1-丛的同伦等价类群。