Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Abelian and nondiscrete convergence groups on the circle

Author: A. Hinkkanen
Journal: Trans. Amer. Math. Soc. 318 (1990), 87-121
MSC: Primary 30C62; Secondary 20H10, 22A99, 30F35
MathSciNet review: 1000145
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A group $ G$ of homeomorphisms of the unit circle onto itself is a convergence group if every sequence of elements of $ G$ contains a subsequence, say $ {{\text{g}}_n}$, such that either (i) $ {{\text{g}}_n} \to {\text{g}}$ and $ {\text{g}}_n^{ - 1} \to {{\text{g}}^{ - 1}}$ uniformly on the circle where $ {\text{g}}$ is a homeomorphism, or (ii) $ {{\text{g}}_n} \to {{\text{x}}_0}$ and $ {\text{g}}_n^{ - 1} \to {{\text{y}}_0}$ uniformly on compact subsets of the complements of $ \{ {{\text{y}}_0}\} $ and $ \{ {{\text{x}}_0}\} $, respectively, for some points $ {{\text{x}}_0}$ and $ {{\text{y}}_0}$ of the circle (possibly $ {{\text{x}}_0}{\text{ = }}{{\text{y}}_0}$). For example, a group of $ K$-quasisymmetric maps, for a fixed $ K$, is a convergence group. We show that if $ G$ is an abelian or nondiscrete convergence group, then there is a homeomorphism $ f$ such that $ f \circ G \circ {f^{ - 1}}$ is a group of Màbius transformations.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30C62, 20H10, 22A99, 30F35

Retrieve articles in all journals with MSC: 30C62, 20H10, 22A99, 30F35

Additional Information

PII: S 0002-9947(1990)1000145-X
Article copyright: © Copyright 1990 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia