Transactions of the American Mathematical Society

Author(s): Robbert Fokkink; Lex Oversteegen
Journal: Trans. Amer. Math. Soc. 354 (2002), 3743-3755.
MSC (2000): Primary 54F15, 57M10; Secondary 54C10, 55R10
Posted: April 23, 2002
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 54F15, 57M10, 54C10, 55R10

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: 10.1090/S0002-9947-02-03017-9
PII: S 0002-9947(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
Posted: April 23, 2002
Additional Notes: The second author was supported in part by NSF-DMS-0072626
Copyright of article: Copyright 2002, American Mathematical Society

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