| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
We studied group cohomology of Coxeter groups, Artin groups and related groups. As for Coxeter groups, we obtain (1) a vanishing theorem for the p-local homology of Coxeter groups (2) a vanishing theorem for the mod p cohomology of alternating subgroups of finite Coxeter groups. As for Artin groups (3) we determined the second mod 2 homology of arbitrary Artin groups. (2) and (3) are joint works with Ye Liu. Finally, we proved that the adjoint group of an arbitrary Coxeter quandle is both a central extension of a Coxeter group W by a free abelian group and a semi-direct product of the commutator subgroup of a Coxeter group W and a free abelian group.
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