Rigidity for $$C^1$$ C 1 actions on the interval arising from hyperbolicity I: solvable groups
| Autor: | Cristóbal Rivas, C. Bonatti, I. Monteverde, Andrés Navas |
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| Rok vydání: | 2016 |
| Předmět: |
Pure mathematics
Group (mathematics) General Mathematics Image (category theory) 010102 general mathematics Automorphism 01 natural sciences Conjugacy class Solvable group 0103 physical sciences Affine group 010307 mathematical physics 0101 mathematics Abelian group Topological conjugacy Mathematics |
| Zdroj: | Mathematische Zeitschrift. 286:919-949 |
| ISSN: | 1432-1823 0025-5874 |
| DOI: | 10.1007/s00209-016-1790-y |
| Popis: | We consider Abelian-by-cyclic groups for which the cyclic factor acts by hyperbolic automorphisms on the Abelian subgroup. We show that if such a group acts faithfully by \(C^1\) diffeomorphisms of the closed interval with no global fixed point at the interior, then the action is topologically conjugate to that of an affine group. Moreover, in case of non-Abelian image, we show a rigidity result concerning the multipliers of the homotheties, despite the fact that the conjugacy is not necessarily smooth. Some consequences for non-solvable groups are proposed. In particular, we give new proofs/examples yielding the existence of finitely-generated, locally-indicable groups with no faithful action by \(C^1\) diffeomorphisms of the interval. |
| Databáze: | OpenAIRE |
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