Project/Area Number  10640080 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
Geometry

Research Institution  Hiroshima University 
Principal Investigator 
IMAOKA Mitsunori Faculty of Education, Hiroshima University, Professor, 教育学部, 教授 (20031817)

CoInvestigator(Kenkyūbuntansha) 
TAKATA Isao Oshima National College of Martime Technology, Hiroshima University, Associate Professor, 助教授 (30178389)
YOSHIDA Toshio Faculty of Integrated Arts and Sciences, Hiroshima University, Professor, 総合科学部, 教授 (10033854)

Project Fiscal Year 
1998 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 1999 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1998 : ¥700,000 (Direct Cost : ¥700,000)

Keywords  transfer maps / sphere bundles / characteristic classes / projective spaces / homotopy / cohomology / トランスファー写像 / 球面束 / 特性類 / 射影空間 / ホモトピー / コホモロジー / ファイバーバンドル / ホモロジー 
Research Abstract 
In this research, we have developed our study on transfer maps of sphere bundles with stressing the following points : To extend the efficiency of the transfer maps concerning projective spaces ; to apply the results of such transfer maps to investigate various bundles. As some of results, we have got the following : 1. By representing the cofiber of the transfer maps using some Thom spaces, we clarified the methods of computing the einvariants of the transfer maps, and extended some results for the transfer maps related to the projective spaces. 2. We analyzed the cases when a vector bundle is stably equivalent to the sum of line bundles. In such cases the einvariants are represented by using some combinatorics. 3. We applied some sorts of transfer maps to the study on representing of elements in the stable homotopy groups of spheres by framed hypersurfaces. Our results appeared and will appear in : M. Imaoka and K . Kuwana : Stably extendible vector bundles over the quaternionic projective spaces, Hiroshima Math. J. 29(1999), 273279. M. Imaoka and K. Knapp : Transfer maps of sphere bundles, J. Math. Soc. Japan, 52(2000), in print.
