Global Rigidity of Solvable Group Actions on S Lizzie Burslem and Amie Wilkinson
نویسنده
چکیده
In this paper we find all solvable groups that act effectively on the circle as realanalytic diffeomorphisms, and we find all of their actions. Our starting point is the procedure of ramified lifting of group actions with a global fixed point, which we develop in Section 1. To summarize the discussion there, we say that a real analytic map π : S → S is a ramified covering map over p ∈ S if the restriction π to S \ π−1({p}) is a regular covering map onto its image S \ {p}. To any subgroup G < Diff (S1) with the property that γ(p) = p, for all γ ∈ G, and any ramified covering map π over p we then associate a subgroup Ĝ < Diff (S1), the π-ramified lift of G, whose elements are the real-analytic lifts under π of elements of G. Each such Ĝ is abstractly isomorphic to an H-extension of G+, where G+ = Diff ω +(S ) ∩ G, and H is a subgroup of a dihedral group determined by π. Applying this procedure to the affine group
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تاریخ انتشار 2008