The structural stability of topological cocycles

Cocycles of Zm actions on compact metric spaces can be used to construct Rm actions or flows, called suspension flows. A suspension provides a higher-dimensional analog to the familiar flow under a function and we look to this construction as a way of generating interesting Rm flows. Even more importantly, an Rm flow with a free dense orbit has an almost one-to-one extension which is a suspension [6] and thus suspensions can be used to model general Rm flows. In this paper we examine the sensitivity of the suspension construction to small perturbations in the cocycle. Theorem 4.7 establishes the fact that two cocycles that are sufficiently close yield suspensions that are isomorphic up to a time change.