Actions and irreducible representations of the mapping class group
نویسنده
چکیده
Let G be a countable discrete group. Call two subgroups H1 and H2 of G commensurable if H1 ∩H2 has finite index in both H1 and H2. We say that an action of G on a discrete set X has noncommensurable stabilizers if the stabilizers of any two distinct points of X are not commensurable. We prove in this paper that the action of the mapping class group on the complex of curves has noncommensurable stabilizers. Following a method due to Burger and de la Harpe, this action leads to constructions of irreducible unitary representations of the mapping class group. Mathematics Subject Classifications: Primary 57N05; Secondary 20F38, 22D10, 22D30.
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