On a Nielsen-Thurston classification theory on cluster modular groups (GPS)
Student No.:50
Time:Tue 9:00-10:30, 2017-7-11
Instructor:Ishibashi Tsukasa  [Tokyo University]
Place:Conference room 3, Floor 2, Jin Chun Yuan West Building
Starting Date:2017-7-11
Ending Date:2017-7-11




It is known that each element of the mapping class group of a orientable surface is classified into three types. These types are characterized by fixed point properties of a natural action on a closed disk, which is the Thurston compactification of the Teichmuller space. These are the Nielsen-Thurston classification thoery. On the other hand, the mapping class group and the Teichmuller space of a surface are generalized to the cluster modular group and the cluster ensemble respectively, by Fock-Goncharov. For a particular choice of the input data, these concepts can describe higher Teichmuller space and the mapping class group action on it in combinatorial languages.

In this talk, I will give a classification of elements of the cluster modular group, which is an analogue of the Nielsen-Thurston classification. Then I relate them with fixed point properties of its action on the cluster ensemble.




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