Algebraic & Geometric Topology

Bihomogeneity of solenoids

Alex Clark and Robbert Fokkink

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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.

Article information

Source
Algebr. Geom. Topol., Volume 2, Number 1 (2002), 1-9.

Dates
Received: 22 August 2001
Revised: 8 January 2002
Accepted: 10 January 2002
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882681

Digital Object Identifier
doi:10.2140/agt.2002.2.1

Mathematical Reviews number (MathSciNet)
MR1885212

Zentralblatt MATH identifier
0995.54025

Subjects
Primary: 54F15: Continua and generalizations
Secondary: 55R10: Fiber bundles

Keywords
homogeneous continuum covering space profinite group principal bundle

Citation

Clark, Alex; Fokkink, Robbert. Bihomogeneity of solenoids. Algebr. Geom. Topol. 2 (2002), no. 1, 1--9. doi:10.2140/agt.2002.2.1. https://projecteuclid.org/euclid.agt/1513882681


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