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2011 $C^1$–actions of Baumslag–Solitar groups on $S^1$
Nancy Guelman, Isabelle Liousse
Algebr. Geom. Topol. 11(3): 1701-1707 (2011). DOI: 10.2140/agt.2011.11.1701

Abstract

Let BS(1,n)=a,baba1=bn be the solvable Baumslag–Solitar group, where n2. It is known that BS(1,n) is isomorphic to the group generated by the two affine maps of the line: f0(x)=x+1 and h0(x)=nx. The action on S1= generated by these two affine maps f0 and h0 is called the standard affine one. We prove that any faithful representation of BS(1,n) into Diff1(S1) is semiconjugated (up to a finite index subgroup) to the standard affine action.

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Nancy Guelman. Isabelle Liousse. "$C^1$–actions of Baumslag–Solitar groups on $S^1$." Algebr. Geom. Topol. 11 (3) 1701 - 1707, 2011. https://doi.org/10.2140/agt.2011.11.1701

Information

Received: 28 October 2010; Revised: 6 April 2011; Accepted: 9 April 2011; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1221.37048
MathSciNet: MR2821437
Digital Object Identifier: 10.2140/agt.2011.11.1701

Subjects:
Primary: 37C85
Secondary: 37E10, 57S25

Rights: Copyright © 2011 Mathematical Sciences Publishers

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