| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
Every closed orientable 3-manifold can be decomposed into 2 handlebodies by cutting it along a closed orientable surface of genus g. This decomposition is called a Heegaard splitting. Given a Heegaard splitting, the group of isotopy classes of orientation-preserving self-homeomorphisms of the 3-manifold that preserve the splitting is called the Goeitz group of the splitting. The aim of this project was to provide a finite presentation of the Goeritz group for every reducible genus-2 Heegaard splitting, and it has completed successfully. As applications or related topics, we obtained the following: (1) a sufficient condition that the Goeritz group of a higher genus Heegaard splitting admits a finite generationg set; (2) the "uniqueness" of (1,1)-decompositions of 2-bridge knots; (3) a characterization of "knotted" subspaces in terms of "relative" homotopy type of knots in the subspaces.
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