2000 Fiscal Year Final Research Report Summary
Hopf invariants and their application
| Project/Area Number |
11640084
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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 | KYUSHU UNIVERSITY |
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Principal Investigator |
IWASE Norio KYUSHU UNIVERSITY Faculty of Mathematics, Ass. Prof., 大学院・数理学研究院, 助教授 (60213287)
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| Co-Investigator(Kenkyū-buntansha) |
SUMI Toshio Kyushu Jastrtute of Derigh Ass. Prof., 助教授 (50258513)
ISHIKAWA Nobahiro KYUSHU UNIVERSITY Faculty of Mathematic, Prof., 大学院・数理学研究院, 教授 (10037806)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Hopf invariant / L-S Category / Square ring / loop space / A_∞-structure |
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| Research Abstract |
1. We obtained an affirmative answer to "the Ganea conjecture" on co-H-space of low dimensions, In the proof, we found an fundamental theorem on a co-Hopf space, However a counter-example was found in higher dimensions, The above fundamental theorem is used to show the example is a co-H-space.
2. L-S category - a numrical invariant defined by Lusternik and Schnirelmann is studied in terms of "higher Hopf inuariuat" and "A_∞-structures on loop spaces". As a result, we found a counter exampled to Gamea's conjecture on L-S category as a simply connected closed manifold.
3. when a space X is in "meta stable" range, End (ΣX) is not a ring but a "square" ring. We determine the structure of End (ΣX) completely in terms of a Hopf invariant, if X is a mapping cone of a sphere-mapping (in meta stable range).
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