| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
I obtained some results on CAT(0) groups, CAT(0) spaces, their boundaries, Coxeter groups and graph theory. First, in the case that a group acts geometrically (i.e. cocompactly, properly discontinuously and by isometries) on two proper CAT(0) spaces, I gave a sufficient condition and an equivalent condition of the group actions as there exists an equivariant homeomorphism between the ideal boundaries of the two CAT(0) spaces. In particular, I obtained some results in the case that the CAT(0) group is a Coxeter group. By observing some applications and examples, I obtained a conjecture that some CAT(0) groups with some simple forms will be non-boundary-rigid CAT(0) groups with uncountable many boundaries. Also I obtained some results on reconstructible graphs from investigating corresponding Coxeter groups.
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