Geodesic
C1–actions of Baumslag–Solitar groups on S1
Guelman, Nancy1 ; Liousse, Isabelle2
1IMERL, Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, 11300 Montevideo, Uruguay
2UFR de Mathématiques, UMR CNRS 8524, Université de Lille 1, Laboratoire Paul Painlevé, 59655 Villeneuve d’Ascq, France
Algebraic and Geometric Topology, Tome 11 (2011) no. 3, pp. 1701-1707
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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.

DOI : 10.2140/agt.2011.11.1701
Classification : 37C85, 57S25, 37E10
Keywords: circle diffeomorphism, solvable Baumslag–Solitar group

Guelman, Nancy  1   ; Liousse, Isabelle  2

1 IMERL, Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, 11300 Montevideo, Uruguay
2 UFR de Mathématiques, UMR CNRS 8524, Université de Lille 1, Laboratoire Paul Painlevé, 59655 Villeneuve d’Ascq, France 
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Guelman, Nancy; Liousse, Isabelle. C1–actions of Baumslag–Solitar groups on S1. Algebraic and Geometric Topology, Tome 11 (2011) no. 3, pp. 1701-1707. doi: 10.2140/agt.2011.11.1701

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