Rank-1 Phenomena for Mapping Class Groups
نویسنده
چکیده
We prove that every element of the mapping class group g has linear growth (confirming a conjecture of N. Ivanov) and that g is not boundedly generated. We also provide restrictions on linear representations of g and its finite index subgroups.
منابع مشابه
Rank one phenomena for mapping class groups
Let Σg be a closed, orientable, connected surface of genus g ≥ 1. The mapping class group Mod(Σg) is the group Homeo(Σg)/Homeo0(Σg) of isotopy classes of orientation-preserving homeomorphisms of Σg. It has been a recurring theme to compare the group Mod(Σg) and its action on the Teichmüller space T (Σg) to lattices in simple Lie groups and their actions on the associated symmetric spaces. Indee...
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تاریخ انتشار 2000