| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Outline of Final Research Achievements |
(1) For 3-submanifolds of the 3-sphere, we studied and obtained results on ①trivialization of knots in it by a homotopy, ②relation between the existence of Seifert surfaces and Dehn surgery along links, ③realization of Fox's re-embeddings by twistings.
(2) From embeddings of multibranched surfaces into 3-manifolds, we defined the genus of it, and showed that the genus is bounded by the sum of the number of branches and sectors above.
(3) We constructed knots with destabilized bridge spheres of arbitrary high bridge number.
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