1999 Fiscal Year Final Research Report Summary
Study on Geometrical properties of bundles using transfer maps and it's application
| Project/Area Number |
10640080
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Hiroshima University |
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Principal Investigator |
IMAOKA Mitsunori Faculty of Education, Hiroshima University, Professor, 教育学部, 教授 (20031817)
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| Co-Investigator(Kenkyū-buntansha) |
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)
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| Project Period (FY) |
1998 – 1999
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| Keywords | transfer maps / sphere bundles / characteristic classes / projective spaces / homotopy / cohomology |
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| 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 e-invariants 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 e-invariants 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), 273-279.
M. Imaoka and K. Knapp : Transfer maps of sphere bundles, J. Math. Soc. Japan, 52(2000), in print.
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