Algebraic & Geometric Topology

Bihomogeneity of solenoids

Alex Clark and Robbert Fokkink

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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

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

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

homogeneous continuum covering space profinite group principal bundle


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

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