Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Published electronically: April 23, 2002
MathSciNet review: 1911519
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 54F15, 57M10, 54C10, 55R10

Retrieve articles in all journals with MSC (2000): 54F15, 57M10, 54C10, 55R10


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: http://dx.doi.org/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
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