2002 Fiscal Year Final Research Report Summary
Representations of 3-manifolds and geometric informations derived from them
| Project/Area Number |
12640071
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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 | Nara Women's University |
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Principal Investigator |
KOBAYASHI Tsuyoshi Nara Women's U.Faculty of Sci., Professor, 理学部, 教授 (00186751)
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| Co-Investigator(Kenkyū-buntansha) |
KATAGIRI Minnyou Nara Women's U.Faculty of Sci., Assoc.Professor, 理学部, 助教授 (60263422)
YAMASHITA Yasushi Nara Women's U.Faculty of Sci., Assis.Professor, 理学部, 講師 (70239987)
OCHIAI Mitsuyuki Nara Women's U.Graduate Sch., Professor, 人間文化研究科, 教授 (70016179)
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| Project Period (FY) |
2000 – 2002
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| Keywords | Heegaard splitting / 3-manifold / knot / Tunnel number / Dehn twist / Ricci curvature / Einstein metric |
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| Research Abstract |
1. Graphic of 3-manifolds
Kobayashi make use of the graphic defined by Rubinstein-Scharlemann to give a complete classification of Heegaard splittings of the exteriors of the 2-bridge knots.
2. Local detection of strong irreducibility of Heegaard splittings by using knot exteriors
Kobayashi together with, Yo'av Rieck analyzed how strongly irreducible Heegaard splittings can intersect the exteriors of non-trivial knots in the 3-sphere and showed that such Heegaard surface intersect the knot exteriors in meridional annuli.
3. Research on Morimoto's Conjecture
Kobayashi together with Yo'av Rieckstudied about Morimoto's Conjecture concerned with the connectedsums of knots in 3-manifolds and the tunnel numbers.
4. Algorithm for decompositions of attaching homeomorphisms of Heegaard splittings into Dehn twists
Ochiai gave an algorithm for giving a decomposition of given attaching homeomorphisms of genus two Heegaard splittings into standard Dehn twists.
5. Moduli space of metrics of Riemannian manifolds
Katagiri studied about Riemannian functional via Ricci curvature and showed that Einstein metric is a critical point of this functional, however there exist critical points that are not Einstein metric. He also gave a sufficient condition for critical points to be Einstein metrics.
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