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Homogeneous weak solenoids


Authors: Robbert Fokkink and Lex Oversteegen
Journal: Trans. Amer. Math. Soc. 354 (2002), 3743-3755
MSC (2000): Primary 54F15, 57M10; Secondary 54C10, 55R10
DOI: https://doi.org/10.1090/S0002-9947-02-03017-9
Published electronically: April 23, 2002
MathSciNet review: 1911519
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Abstract: A (generalized) weak solenoid is an inverse limit space over manifolds with bonding maps that are covering maps. If the covering maps are regular, then we call the inverse limit space a strong solenoid. By a theorem of M.C. McCord, strong solenoids are homogeneous. We show conversely that homogeneous weak solenoids are topologically equivalent to strong solenoids. We also give an example of a weak solenoid that has simply connected path-components, but which is not homogeneous.


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Additional Information

Robbert Fokkink
Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294

Lex Oversteegen
Affiliation: Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama 35294
Email: overstee@vorteb.math.uab.edu

DOI: https://doi.org/10.1090/S0002-9947-02-03017-9
Keywords: Homogeneous continuum, solenoid, covering space, profinite group, principal bundle
Received by editor(s): April 4, 2001
Received by editor(s) in revised form: January 4, 2002
Published electronically: April 23, 2002
Additional Notes: The second author was supported in part by NSF-DMS-0072626
Article copyright: © Copyright 2002 American Mathematical Society

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