2013 Fiscal Year Final Research Report
Low-dimensional topological invariants, hyperbolic volume and Perelman invariants
| Project/Area Number |
21540069
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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 | Chiba University |
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Principal Investigator |
KUGA Ken-ichi 千葉大学, 理学(系)研究科(研究院), 教授 (30186374)
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| Co-Investigator(Kenkyū-buntansha) |
INABA Takashi 千葉大学, 大学院理学研究科, 教授 (40125901)
SUGIYAMA Ken-ichi 千葉大学, 大学院理学研究科, 教授 (90206441)
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| Project Period (FY) |
2009-04-01 – 2014-03-31
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| Keywords | 低次元位相不変量 / 双曲体積 |
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| Research Abstract |
We investigated the possibility of applying the technique of Hamilton's Ricci flow to the understanding of the topology of 4 dimensional manifolds, or more generally, to the understanding of various topological invariants in low-dimensional topology. While in dimension three, the formation of singularities is well understood due to the works of Hamilton and Perelman,in dimension 4, the singularity seems unstable with respect to the initial metiric, which eventually prevented our systematic understanding of the formation in dimension 4 during this period of study. Some peripheral computation concerning Khovanov homology of some links were performed.
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