$C^1$-actions of Baumslag-Solitar groups on $S^1$

Abstract

Let $BS(1,n)=<a,b|ab{a}^{-1}=b^n>$ be the solvable Baumslag-Solitar group, where $n\ge 2$. It is known that B(1, n) is isomorphic to the group generated by the two affine maps of the line : $f_0(x)=x+1$ and $h_0(x)=nx$. The action on $S^1 = \RR \cup {\infty}$ generated by these two affine maps $f_0$ and $h_0$ is called the standard affine one. We prove that any representation of BS(1,n) into $Dif{f}^1(S^1)$ is (up to a finite index subgroup) semiconjugated to the standard affine action.

References in corpus (1)

• A finitely generated, locally indicable group with no faithful action by C^1 diffeomorphisms of the interval

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