2000 Fiscal Year Final Research Report Summary
Spin^c Analysis for Group C^*-bundles on Manifolds and Study of Yamabe Invariants
| Project/Area Number |
11640070
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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 | Shizuoka University |
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Principal Investigator |
AKUTAGAWA Kazuo Shizuoka University, Faculty of Science, Associated Professor, 理学部, 助教授 (80192920)
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| Co-Investigator(Kenkyū-buntansha) |
KUMURA Hironori Shizuoka University, Faculty of Science, Full-Time Lecturer, 理学部, 講師 (30283336)
OKUMURA Yoshihide Shizuoka University, Faculty of Science, Associated Professor, 理学部, 助教授 (90214080)
HIROKI Sato Shizuoka University, Faculty of Science, Professor, 理学部, 教授 (40022222)
IZEKI Hiroyasu Tohoku University, Graduate School of Science, Associated Professor, 大学院・理学研究科, 助教授 (90244409)
ONO Kaoru Hokkaido University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (20204232)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Yamabe Invariant / Conformal Geometry / Differential Topology / Symplectic Geometry / Spin^c Geometry / Descrete Group / Cobordism / Manifolds of Negative Curvature |
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| Research Abstract |
We studied on Spin^c Analysis for Group C^*-bundles on Manifolds and Yamabe Invariants.
More precisely, we studied on the fundamentals of C^*-algebras and their K-theory. We also studied on the synthetic research of Yamabe invariants and Bordism theory with supergroups (i.e., supergroups, supergroup-structures on manifolds, supergroup C^*-bunbles and others). In particular, by using this bordism theory with supergroups, we obtained an obstruction to the positivity of relative Yamabe invariants. This result is written in the following paper :
Kazuo Akutagawa, An obstruction to the positivity of relative Yamabe invariants.
The head investigator, Kazuo Akutagawa also studied with professor Boris Botvinnik (University of Oregon) on Yamabe invariants from the algebraic topological viewpoint. Similar to the Homology theory, we defined a natural relative version of the Yamabe invariant, that is, the "relative Yamabe invariant", and we studied on it and the relation of the Yamabe invariant of a double manifold. This result is also written in the following papers :
Kazuo Akutagawa and Boris Botvinnik, Relative Yamabe invariant.
Kazuo Akutagawa and Boris Botvinnik, Manifolds of positive scalar curvature and conformal cobordism theory.
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