Journal ArticleDOI
Groups of homeomorphisms of the line and the circle. Topological characteristics and metric invariants
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In this paper, a survey of topological, algebraic, and combinatorial properties of metric invariants for arbitrary groups of homeomorphisms of the line and the circle is presented.Abstract:
This survey is devoted to investigations concerning topological, algebraic, and combinatorial characteristics as well as metric invariants for arbitrary groups of homeomorphisms of the line and the circle. Relationships between these characteristics are established, the most important metric invariants are studied (in the form of invariant, projectively invariant, and ω-projectively invariant measures), and the main 'obstructions' to the existence of metric invariants of this kind are described.read more
Citations
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On the dynamics of (left) orderable groups
TL;DR: In this article, the authors define le noyau conradien d'un ordre comme andant le plus grand sous-groupe convexe sur lequel the relation is conradienne, and nous travaillons avec cette notion.
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Milnor's Problem on the Growth of Groups and its Consequences
TL;DR: A survey of results related to the Milnor's problem on group growth is presented in this paper, where a number of related topics (growth of manifolds, amenability, asymptotic behavior of random walks) are considered.
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On the dynamics of (left) orderable groups
TL;DR: The notion of the Conradian soul of an order as the maximal subgroup which is convex and restricted to which the original ordering satisfies the so-called conradian property was introduced in this article.
Journal ArticleDOI
Classification of the group actions on the real line and circle
TL;DR: In this article, it was shown that each minimal continuous action of a group on the circle is either a conjugate of an isometric action, or a finite cover of a proximal action.
Journal ArticleDOI
Structure theorems for groups of homeomorphisms of the circle
TL;DR: The set of groups of orientation-preserving homeomorphisms of the circle S1 which do not admit non-abelian free subgroups is studied to derive various new and old results about the groups in .
References
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