2000 Fiscal Year Final Research Report Summary
Topology related to Mathematical Physics and Numerical Computations
| Project/Area Number |
11640066
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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 | The University of Electro-Commnications |
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Principal Investigator |
KOHHEI Yamaguchi Univ. Electro-Commun., Department of Electro-Commun., Professor, 電気通信学部, 教授 (00175655)
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| Co-Investigator(Kenkyū-buntansha) |
OHNO Masahiro Univ. Elec.-Commun. Fac. Elect.-Commun., Asso. Prof., 電気通信学部, 助教授 (70277820)
KIDA Masonari Univ. Elec.-Commun. Fac. Elect.-Commun., Asso. Prof., 電気通信学部, 助教授 (20272057)
NAITO Toshiki Univ. Elec.-Commun. Fac. Elect.-Commun., Professor, 電気通信学部, 教授 (60004446)
YAMADA Yuichi Univ. Elec.-Commun. Fac. Elect.-Commun., Lecturer, 電気通信学部, 講師 (30303019)
MISAWA Masashi Univ. Elec.-Commun. Fac. Elect.-Commun., Lecturer, 電気通信学部, 講師 (40242672)
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| Project Period (FY) |
1999 – 2000
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| Keywords | topology / homotopy / polynomial / configuration space / harmonic map / variety / homotopy sphere / weak solution |
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| Research Abstract |
The main purpose of K.Yamaguchi is to study the topologies of labelled configuration spaces. Nowdays he and Kozlowski found that the Morse theoretic principle holds for the space P^d_n(C), where P^d_n(C) denotes the space consisting of all monic polynomials f(z) ∈ C [z] of dgree d without real roots of multiplicity 【greater than or equal】 n. It follows from the above results that we knew that Morse theoretic principle (which is also called as Smale-Hirsh principle) holds for these cases and that it also sometimes holds even in the infinite dimensional cases. Similarly, we investigated the topology of spaces of holomorphic maps from Riemann surface to complex projective space with bounded multiplicity case. In this case, we found that similar Morse theoretic principle also holds. Finally, concerning to the latter subject, he noticed the group structure of the group of self- homotopy equivalences of SO(4) and published it too. M.Ohno studied the vector bundles over non-singular projective varieties and investigated them from the point of view of "nef value". Y.Yamada studied the topology of 4-manifolds and obtained several results related to Gluck surgery. M.Misawa studied the valation principle related to harmonic maps from the point of view of partial differential equation. In particular, he found the existence and regurality of p-harmonic maps (weak solution).
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