Algebraic and Geometric Topology 2 (2002), paper no. 1, pages 1-9.

Bihomogeneity of solenoids

Alex Clark, Robbert Fokkink

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

AMS subject classification. Primary: 54F15. Secondary: 55R10.

DOI: 10.2140/agt.2002.2.1

E-print: arXiv:math.DS/0201287

Submitted: 22 August 2001. (Revised: 8 January 2002.) Accepted: 10 January 2002. Published: 12 January 2002.

Notes on file formats

Alex Clark, Robbert Fokkink
University of North Texas, Department of Mathematics
Denton TX 76203-1430, USA
Technische Universiteit Delft, Faculty of Information Technology and Systems
Division Mediamatica, P.O. Box 5031, 2600 GA Delft, Netherlands


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