1998 Fiscal Year Final Research Report Summary
On multiplicative genera related to deformation of smooth manifolds
| Project/Area Number |
09440036
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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 |
KAMATA Masayoshi Kyushu Univ., G.S.of Math., Professor, 大学院・数理学研究科, 教授 (60038495)
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| Co-Investigator(Kenkyū-buntansha) |
HARA Tamio Tokyo Sci.Univ., Mathematics Research Associate, 理工学部, 助手 (10120205)
NISHI Haruko Kyushu Univ., G.S.of Math., Research Associate, 大学院・数理学研究科, 助手 (90274430)
TAKATA Toshie Kyushu Univ., G.S.of Math., Assistant Professor, 大学院・数理学研究科, 講師 (40253398)
YOKOTA Yosiyuki Kyushu Univ., G.S.of Math., Assistant Professor, 大学院・数理学研究科, 講師 (40240197)
IWASE Norio Kyushu Univ., G.S.of Math., Associate Professor, 大学院・数理学研究科, 助教授 (60213287)
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| Project Period (FY) |
1997 – 1998
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| Keywords | cobordism group / SKgroup / genus / framed cobordism / LS-category / Hopf invariant / homotopy group / quantum invariant |
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| Research Abstract |
We studied characterization of smooth manifolds by topological invariants. We mainly invetigated multiplicative genera, Euler numbers, quantum invariants and so on. Further-more we studied the related generalized cohomology and homotopy group. Kamata obtained the condition of cobordism equivalence between projective spaces associated to U(1) -representation spaces. Lie groups are stably frat and the framed cobordism classes are in-terpreted as the stable homotopy classes of a sphere. Kamata and Minami used the J-group to prove that the special orthogonal group SO(2n) is the boundary of a compact smooth manifold with the stably trivial tangent bundle. LS category is related to the estimate of the number of critical points of the Morse function on a smooth manifold. Iwase defined the generalized Hopf invariant concerned with the LS category and showed many counterexam-pies of Ganea conjecture which is a open question for LS category. Hara treated the surgery of equvariant Z_<2r> manifolds and he completely determined the classes of manifolds under the classification concerned with cutting and pasting. Maruyama and Arkowitz studied the classes of seif-homotopy equivalence with the homological condition and showed the method of computation of the number of the classes. It is a conjecture that the quantum invariants of 3-dimensional manifolds defined for a compact Lie group are evaluated in an algebraic integer ring. Yokota and Takata proved that the conjecture is correct for the special unitary group SU(N). Nishi discussed the hyperbolization of the configuration space of n(<greater than or equal>5) marked points with weights in the projective line up to projective transformat
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