Dynamical forcing of circular groups
| dc.creator | Calegari, Danny | |
| dc.date | 2003-12-03 | |
| dc.date | 2004-09-09 | |
| dc.date.accessioned | 2026-07-07T06:29:28Z | |
| dc.date.available | 2026-07-07T06:29:28Z | |
| dc.description | In this paper we introduce and study the notion of dynamical forcing. Basically, we develop a toolkit of techniques to produce finitely presented groups which can only act on the circle with certain prescribed dynamical properties. As an application, we show that the set X of rotation numbers which can be forced by finitely presented groups is an infinitely generated Q-module, containing countably infinitely many algebraically independent transcendental numbers. We also show that the set of subsets of the circle which are the set of rotation numbers of an element g of a group G under all actions of G on a circle, as G varies over all countable groups, are exactly the set of closed subsets of the circle which contain 0, and are invariant under the involution which interchanges x and -x. As another application, we construct a finitely generated group which acts faithfully on the circle, but which does not admit any faithful C^1 action, thus answering in the negative a question of John Franks. | |
| dc.description | 18 pages (v3: typos corrected) | |
| dc.identifier | https://arxiv.org/abs/math/0312066 | |
| dc.identifier | http://arxiv.org/abs/math/0312066 | |
| dc.identifier | Trans. Amer. Math. Soc. 358 (2006), no. 8, 3473-3491 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/98043 | |
| dc.subject | Group Theory | |
| dc.subject | Dynamical Systems | |
| dc.title | Dynamical forcing of circular groups | |
| dc.type | text |