2003 Fiscal Year Final Research Report Summary
Heegaad splittings of 3-dimensional manifolds and geometric structures
| Project/Area Number |
12440018
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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 | OSAKA UNIVERSITY |
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Principal Investigator |
NAMBA Makoto NAMBA,Makoto, 大学院・理学研究科, 教授 (60004462)
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| Co-Investigator(Kenkyū-buntansha) |
WADA Masaaki Nara Women's Univ., Fac. of Sci., Professor, 理学部, 教授 (80192821)
SAKUMA Makoto SAKUMA,Makoto, 大学院・理学研究科, 助教授 (30178602)
KONNO Kazuhiro KONNO,Kazuhiro, 大学院・理学研究科, 教授 (10186869)
KOMORI Yohei Osaka city Univ., Sch. of Sci., Assistant, 理学研究科, 助手 (70264794)
YAMASHITA Yasushi Nara Women's Univ., Fac. of Sci., Instructor, 理学部, 講師 (70239987)
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| Project Period (FY) |
2000 – 2003
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| Keywords | fundamental group / finite Galois coverings / Zariski pair / hyperbolic manifolds / punctured torus / Epstein-Penner docomposition / McShane's indentity / quasifuchisian space |
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| Research Abstract |
(1)Fundamental groups and branched coverings. M.Namba gave with H.Tsuchihashi a method for concrete computations of fundamental groups of the compliments of curves in the complex projective plane and finite branched Galois coverings branching along the curves, and gave a new example of Zariski pair using the method.
(2)Generaliztion of Epsein-Penner decomposition. H.Akiyoshi and M.Sakuma gave a generalization of the Epstein-Penner decompositions of cusped hyperbol manifolds of finite volume to those of infinite volume, and studied relation with the convex cores. They collaborated with M.Wada and Y.Yamashita and gave partial answer and experimental evidences to their conjecture that the pleating loci would determine the generalized Epstein-Pener decompositions for punctured torus groups.
(3)H.Akiyoshi, M.Miyachi and M.Sakuma have established a variation of McShane's identity for punctued surface bundles over a circle, which expresses the modulus of cusptori in terms of the complex translation lengths of essential simple loops of the fiber surfaces.
(4)Drawing the 3D slices of the quasifuchsian punctured torus space. M.Wada and Y.Yamashita developed a software to draw (real) 3-dimensional slices of the quasifuchsian punctured torus space
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