Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 11, Number 3 (2011), 1701-1707.
$C^1$–actions of Baumslag–Solitar groups on $S^1$
Let be the solvable Baumslag–Solitar group, where . It is known that is isomorphic to the group generated by the two affine maps of the line: and . The action on generated by these two affine maps and is called the standard affine one. We prove that any faithful representation of into is semiconjugated (up to a finite index subgroup) to the standard affine action.
Algebr. Geom. Topol., Volume 11, Number 3 (2011), 1701-1707.
Received: 28 October 2010
Revised: 6 April 2011
Accepted: 9 April 2011
First available in Project Euclid: 19 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 37C85: Dynamics of group actions other than Z and R, and foliations [See mainly 22Fxx, and also 57R30, 57Sxx]
Secondary: 57S25: Groups acting on specific manifolds 37E10: Maps of the circle
Guelman, Nancy; Liousse, Isabelle. $C^1$–actions of Baumslag–Solitar groups on $S^1$. Algebr. Geom. Topol. 11 (2011), no. 3, 1701--1707. doi:10.2140/agt.2011.11.1701. https://projecteuclid.org/euclid.agt/1513715241