2013 Fiscal Year Final Research Report
Topological complexity and L-S theory
| Project/Area Number |
22340014
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Kyushu University |
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Principal Investigator |
IWASE NORIO 九州大学, 数理(科)学研究科(研究院), 教授 (60213287)
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| Co-Investigator(Kenkyū-buntansha) |
SUMI Toshio 九州大学, 基幹教育院, 准教授 (50258513)
SAKAI Michihiro 久留米工業高等専門学校, 准教授 (90353276)
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| Co-Investigator(Renkei-kenkyūsha) |
KONO Akira 同志社大学, 理学部, 教授 (00093237)
SAEKI Osamu 九州大学, マス・フォア・インダストリ研究所, 教授 (30201510)
KAMIYAMA Yasuhiko 琉球大学, 理学部, 教授 (10244287)
TAMAKI Dai 信州大学, 理学部, 教授 (10252058)
TSUKUDA Shuichi 琉球大学, 理学部, 准教授 (50305182)
KISHIMOTO Daisuke 京都大学, 理学研究科, 准教授 (30201510)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 位相的複雑さ / 単位位相的複雑さ / L-S カテゴリ / ホップ不変量 / fibrewise 理論 / C_k-空間 / ギャップ群 / Laitinen 予想 |
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| Research Abstract |
Sakai and Iwase showed the folloing. 1) A space X with cat(X) less than or equal to k is an H-space if and only if X is a C_k soace. Moreover, a C_1 space with at most three cells other than the base point is an H-space. 2) A monoidal topological complexity differs from the original topological complexity at most by 1. 3) The L-S category of a rotation group coincides with its cup-length. 4) L-S category is less than or equal to 1 if and only if p-localized version of L-S category has the same property for every prime p, where we do not need to assume that the space is simply-connected. Further Sumi et al gave 5) a necessary and sufficient condition for a finite group G to be a gap group, unless the first homology group H_1(G) is a 2-group and showed 6) The Laitinen conjecture is true for any finite non-solvable groups except for Aut(A_6).
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Research Products
(51 results)
