Algebraic & Geometric Topology 11 (2011) 1701–1707

DOI: 10.2140/agt.2011.11.1701

Abstract

Let BS(1,n) = 〈a,b∣aba⁻¹ = bⁿ〉 be the solvable Baumslag–Solitar group, where n ≥ 2. 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 = R ∪∞ 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.

Keywords

circle diffeomorphism, solvable Baumslag–Solitar group

Mathematical Subject Classification

Primary: 37C85

Secondary: 37E10, 57S25

References

Publication

Received: 28 October 2010
Revised: 6 April 2011
Accepted: 9 April 2011
Published: 3 June 2011

Authors