2005 Fiscal Year Final Research Report Summary
Hecguard Splittings and genetic structures of 3-manifolds
| Project/Area Number |
14340023
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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 |
SAKUMA Makoto Osaka University, Graduate school of Science, Associate Professor, 理学研究科, 助教授 (30178602)
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| Co-Investigator(Kenkyū-buntansha) |
AKIYOSHI Hirotaka Osaka City Univ., Graduate school of Science, Associate Prof., 大学院・理学研究科, 特任助教授 (80397611)
WADA Masaki Nara Women's Univ., Faculty of Science, Prof., 理学部, 教授 (80192821)
YAMASHITA Yasushi Nara Women's Univ., Faculty of Science, Associate Prof., 理学部, 助教授 (70239987)
OHSHIKA Ken'ichi Osaka Univ., Graduate school of Science, Prof., 理学研究科, 教授 (70183225)
KOBAYASHI Tsuyoshi Nara Women's Univ., Faculty of Science, Prof., 理学部, 教授 (00186751)
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| Project Period (FY) |
2002 – 2005
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| Keywords | quasi-fuchsian group / punctured torus / Hecguard Splittings / Ford domain / 2-bridge knot |
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| Research Abstract |
The main results obtained by this project are as follows.
1.Akiyoshi, Sakuma, Wada and Yamashita have completed a preprint (256 pages) which gives a full exposition of Jorgensen's theory for the Ford domains of quasifuchsian punctured torus groups, including a full proof. We plan to write a sequel of the paper to explain our extension of his theory to the outside of the quasifuchsian punctured torus space and to explain the relationship between the bridge structure of a 2-bridge knot and the complete hyperbolic structure of its complement.
2.Epstein-Penner has introduced the Euclidean decompositions of finite-volume cusped hyperbolic manifolds through a convex hull construction in the Minkowski space. Akiyoshi-Sakuma has generalized the construction to (possibly) infinite-volume cusped hyperbolic manifolds and introduced EPH-decompositions of these manifolds. Moreover, relation between the EPH-decompositions and the bending laminations of cusped hyper-bolic manifolds were studied by Akiyoshi-Sakuma-Wada Yamashita.
3.Akiyoshi-Miyachi-Sakuma have generalized Bowditch's variation of McShane's identity for hyperbolic punctured torus bundles to general hyperbolic punctured surface bundles.
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