Tuesday Seminar on Topology

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Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2014/06/17

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Yoshifumi Matsuda (Aoyama Gakuin University)
Bounded Euler number of actions of 2-orbifold groups on the circle (JAPANESE)
[ Abstract ]
Burger, Iozzi and Wienhard defined the bounded Euler number for a
continuous action of the fundamental group of a connected oriented
surface of finite type possibly with punctures on the circle. A Milnor-Wood
type inequality involving the bounded Euler number holds and its maximality
characterizes Fuchsian actions up to semiconjugacy. The definition of the
bounded Euler number can be extended to actions of 2-orbifold groups by
considering coverings. A Milnor-Wood type inequality and the characterization
of Fuchsian actions also hold in this case. In this talk, we describe when lifts
of Fuchsian actions of certain 2-orbifold groups, such as the modular group,
are characterized by its bounded Euler number.