| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
There are many infinite simple groups which have natural actions on spaces. Consider the set X of the unions of the conjugate classes of a nontrivial element and its inverse in an infinite simple group G. For 2 such unions, one union is always contained in a power of the other. This phenominon gives rise to a metric on X. We studied properties of this metric on X by using the action of G on some space. For a nontrivial subset K which is closed under taking inverses, any element of G can be written as a product of conjugates of elements of K. The minimal number of conjugates defines a norm on the group G. We clarified the relationship between the metric on X and the norm and quasimorphisms on G. We also showed that in certain homeomorphism groups, every elemet can be written as one commutator.
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