Mathematics – Group Theory
Scientific paper
2003-12-03
Trans. Amer. Math. Soc. 358 (2006), no. 8, 3473-3491
Mathematics
Group Theory
18 pages (v3: typos corrected)
Scientific paper
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.
No associations
LandOfFree
Dynamical forcing of circular groups does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Dynamical forcing of circular groups, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical forcing of circular groups will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-187941