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.

储备结果的摘要如下1。我们为任何奇数p构建了p-ther阶mod p不稳定的同胞操作。然后，通过使用该操作，我们研究了Steenrod操作对Mod P有限HOPF空间的共同体的作用。我们在2000年3月2日举行的约翰霍普金斯大学的日本美国数学研究所进行了一部分讲座。为了将上述p-ther阶操作应用于HOPF空间的共同体，我们引入了HOPF空间之间的地图的迭代H-deviation，这是H-Deviation的扩展。3。我们研究了Mod P有限HOPF空间的条件，以进行量化P-prigular。我们的结果被认为是Kumpel对Mod P有限HOPF空间的p频率的概括。我们的结果包括Harper，McClearly和Wilkerson.4的结果。 o ^^ - Shima确定了特殊组G_2的自同时验证等效度的组结构。而莫里苏吉（Morisugi）确定了古典群体SU（3），sp（2）.5。 Shimomura研究了位于Prime 2或3的球体的若υ^<-1> _2bp _2bp占地同型组。KomatsuStudio通过广义投影方法研究了瓷砖空间的轨道闭合分解。 Tsukiyama Studio研究了S^1捆绑的同型等效类别。