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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Bihomogeneity of solenoids

Alex Clark and Robbert Fokkink

Algebraic & Geometric Topology 2 (2002) 1–9

arXiv: math.DS/0201287

Abstract

Solenoids are inverse limit spaces over regular covering maps of closed manifolds. M C McCord has shown that solenoids are topologically homogeneous and that they are principal bundles with a profinite structure group. We show that if a solenoid is bihomogeneous, then its structure group contains an open abelian subgroup. This leads to new examples of homogeneous continua that are not bihomogeneous.

Keywords
homogeneous continuum, covering space, profinite group, principal bundle
Mathematical Subject Classification 2000
Primary: 54F15
Secondary: 55R10
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Publication
Received: 22 August 2001
Revised: 8 January 2002
Accepted: 10 January 2002
Published: 12 January 2002
Authors
Alex Clark
University of North Texas
Department of Mathematics
Denton TX 76203-1430
USA
Robbert Fokkink
Technische Universiteit Delft
Faculty of Information Technology and Systems
Division Mediamatica
PO Box 5031
2600 GA Delft
Netherlands