| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
(1) We showed that one can deform the 2-category structure of the categorified quantum group into a pivotal one. (2) I gave an elementary, direct proof of the fact that the category of finitely generated free groups is freely generated as a symmetric monoidal category by a commutative Hopf monoid. (3) We constructed a functor on the category B of bottom tangles in handlebodies using the Kontsevich invariant, and determined the structure of the associated graded category for the Vassiliev-Goussarov filtration for the linearization of the category B. (4) We generalized the notion of the Johnson filtration and the Johnson homomorphisms for the mapping class groups of surfaces to the context of any action of any group G on any other group K with a filtration.
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