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Convergence groups from subgroups

Eric L Swenson

Geometry & Topology 6 (2002) 649–655

arXiv: math.GN/0212386

Abstract

We give sufficient conditions for a group of homeomorphisms of a Peano continuum X without cut-points to be a convergence group. The condition is that there is a collection of convergence subgroups whose limit sets “cut up" X in the correct fashion. This is closely related to the result in [Topology 39 (2000) 229-237].

Keywords
group, convergence group, Peano continuum
Mathematical Subject Classification 2000
Primary: 20F32
Secondary: 57N10
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Publication
Received: 26 2002
Accepted: 15 November 2002
Published: 14 December 2002
Proposed: David Gabai
Seconded: Benson Farb, Cameron Gordon
Authors
Eric L Swenson
Brigham Young University
Mathematics Department
292 TMCB
Provo
Utah 84604
USA