1999 Fiscal Year Final Research Report Summary
Manifolds with Actions of Cyclic Groups
| Project/Area Number |
10640068
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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 | Yokohama National University |
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Principal Investigator |
KITADA Yasuhiko Yokohama Nat. Univ., Fac. Eng., Prof., 工学部, 教授 (70016145)
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| Co-Investigator(Kenkyū-buntansha) |
HIRANO Norimichi Yokohama Nat. Univ., Grad. School Eng., Prof., 工学研究科, 教授 (80134815)
TAMANO Kenichi Yokohama Nat. Univ., Fac. Eng., Prof., 工学部, 教授 (90171892)
TERADA Toshiji Yokohama Nat. Univ., Grad. School Eng., Prof., 工学研究科, 教授 (80126383)
NISHIMURA Takashi Yokohama Nat. Univ., Fac. Edu. Hum. Sci., Ass. Prof., 教育人間科学部, 助教授 (80189307)
NAGURA Maki Yokohama Nat. Univ., Fac. Eng., Assis., 工学部, 助手 (40251772)
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| Project Period (FY) |
1998 – 1999
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| Keywords | transformation group / surgery / characteristic class / Kervaire class / Steenrod algebra |
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| Research Abstract |
The project team made researches concerning the relation between Kervaire classes in different dimensions in order to utilize the result to obtain informations on surgery obstructions on the quotient manifold with finite cyclic group actions.
1. In May 1999, we announced the newly discovered relation of Kervaire clases :
SqィイD12a+1ィエD1SqィイD12aィエD1SqィイD12a-1ィエD1KィイD22a-2ィエD2 + (SqィイD12a+1ィエD1SqィイD12a-1ィエD1 + SqィイD12a+2a-1ィエD1SqィイD12aィエD1)KィイD22a+1-2ィエD2 = 0
In July 1999, we announced the result concerning smooth Kervaire classes at Topology Conference at Morelia (Mexico) :
A(a, b, c) : SqィイD12bィエD1SqィイD12cィエD1KィイD22a+1-2ィエD2 + SqィイD12a+1ィエD1SqィイD12bィエD1SqィイD12cィエD1KィイD22a-2ィエD2 = O(a > b > c 【greater than or equal】 0)
The paper is submitted to "Topology and its Applications".
3. By symbolic calculation method of computers up to dimension 200, we obtained a conjecture stronger than the one stated in item 1 :
B(a, b) : SqィイD12a+1ィエD1SqィイD12aィエD1SqィイD12bィエD1KィイD22a-2ィエD2 + (SqィイD12a+1ィエD1SqィイD12bィエD1 + ΣィイD4b-1ィエD4ィイD5i=1ィエD5 SqィイD12a+1-2iィエD1SqィイD12b+2iィエD1SqィイD12b+2iィエD1) KィイD22a+1-2ィエD2 = 0 (a > b > 0)
4. The relations A(a, b, c) and B(a, b) account for all the additive 45 relations of Kervaire classes over the mod 2 Steenrod algebra up to dimension 200. We have already made preliminary preparations for B(a, b) and its proof will soon be completed.
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