(Thurston-Sullivan?) Are all smooth actions of $\Phi _g$ on $\mathbb S^1$ which are topologically conjugate to a standard one differentiably conjugate to the standard one?

PermalinkSubmitted by DennisSullivan on Tue, 12/27/2016 - 19:56

assuming we are talking about nielsens action of the mapping class group on the circle at infinity...the only question that I recall makes sense is to show this [ continuous even quasisymmetric ] action is not conjugate to a smooth action [even C1 or even absolutely continuous] because the absolute continuity is the obstruction to mostow rigidity in this dimension [ absolute continuity holding for quasiconformal or quasi symmetric in higher dim.yielding mostow rigidity]

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## FL

Yes. [1]

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## Let the group mean the

assuming we are talking about nielsens action of the mapping class group on the circle at infinity...the only question that I recall makes sense is to show this [ continuous even quasisymmetric ] action is not conjugate to a smooth action [even C1 or even absolutely continuous] because the absolute continuity is the obstruction to mostow rigidity in this dimension [ absolute continuity holding for quasiconformal or quasi symmetric in higher dim.yielding mostow rigidity]

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