Project/Area Number  10640064 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Geometry

Research Institution  Chiba University 
Principal Investigator 
MARUYAMA Kenichi Chiba University, Faculty of Education Associate Professor, 教育学部, 助教授 (70173961)

CoInvestigator(Kenkyūbuntansha) 
TSUKIYAMA Kouzou Shimane University, Faculty of Education, Professor, 教育学部, 教授 (20093651)
KOSHIKAWA Hiroaki Chiba University, Faculty of Education, Professor, 教育学部, 教授 (60000866)
YAMAUCHI Kenichi Chiba University, Faculty of Education, Associate Professor, 教育学部, 助教授 (20009690)

Project Fiscal Year 
1998 – 2000

Project Status 
Completed(Fiscal Year 2000)

Budget Amount *help 
¥2,800,000 (Direct Cost : ¥2,800,000)
Fiscal Year 2000 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1999 : ¥900,000 (Direct Cost : ¥900,000)
Fiscal Year 1998 : ¥1,100,000 (Direct Cost : ¥1,100,000)

Keywords  Algebraic Topology / Homotopy Theory / Nilpotent group / Algebraic Group / 代数的位相幾何学 / ホモトピー論 / 冪零群 / 代数群 / 巾零群論 
Research Abstract 
Supported by the aid we are sure that we have made interesting contribution to homotopy theory in algebric toplology. In the following we summarize our results. First we study the invariance of the group of self homotopy euqivalences of a space on the genus set. We have obtained the result that certain subgroups associated with homotopy groups actually satisfy the invariance property for Hopf spaces. On this result, we gave a talk at the work shop in Italy in September 1999. Secondary, we studied the stability property, so called the MittagLeffler property, of normal series of homotopy sets associated with homotopy groups. We were able to show that the MittagLeffler property holds for rational spaces by using the our previous result which generalizes the results by Sullivan and Wilkerson. Further we have showed that good spaces such as products of spheres or Hopf space have the MittagLeffler property. We are now writing a paper on this result and also we are expecting more reslts in this direction. Thirdly we have observed the above phenomena concretely on spaces whose topologicl properties are well known such as Lie groups. But even among Lie grops of low ranks, it was not an easy task. In many case, the primary obstruction is that we do not have sufficient information on their homotopy groups. Therefore we have carried out computation of unstable homotopy groups of spheres along the methods of Toda. Other coworkers also have made contribution to this project and obtained excellent results on their fields as well. 上記項目を具体的な例で調べた。この目的のために、リー群などの位相的な性質のよく分かっている空間を利用することにしたが、たとえ低いランクのリー群に限っても、たとえば項目2で述べた事柄を確認することは相当な困難を伴うことが判明してきた。その過程で球面のホモトピー群の決定が是非とも必要となってきたので、特に3成分についての計算を実行し、結果を得た。 4.研分担者の成果 本研究は、代表者以外に3人の研究分担者の協力のもとに推進された。研究分担者はそれぞれの研究において大きな成果を得た。
