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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A covering cocycle which does not grow linearly


Author: Kathleen M. Madden
Journal: Trans. Amer. Math. Soc. 347 (1995), 2225-2234
MSC: Primary 28D10; Secondary 54H20, 58F11
MathSciNet review: 1277127
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Abstract: A cocycle $ h:X \times {Z^m} \to {R^n}$ of a $ {Z^m}$ action on a compact metric space, provides an $ {R^n}$ suspension flow (analogous to a flow under a function) on a space $ {X_h}$ which may not be Hausdorff or even $ {T_1}$. Linear growth of $ h$ guarantees that $ {X_h}$ is a Hausdorff space; when $ m = n$, linear growth is a consequence of $ {X_h}$ being Hausdorff and a covering condition. This paper contains the construction of a cocycle $ h:X \times Z \to {R^2}$ which does not grow linearly yet produces a locally compact Hausdorff space with the covering condition. The $ Z$ action used in the construction is a substitution minimal set.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1995-1277127-0
Article copyright: © Copyright 1995 American Mathematical Society