A covering cocycle which does not grow linearly

Madden, Kathleen M.

doi:10.1090/S0002-9947-1995-1277127-0

A covering cocycle which does not grow linearly
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by Kathleen M. Madden PDF

Trans. Amer. Math. Soc. 347 (1995), 2225-2234 Request permission

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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