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Abstract

Our interest in this work is in group extensions of minimal flows with compact abelian groups in the fibres. We study their structure from the categorical and algebraic points of view, and describe relations of their dynamics to one-dimensional algebraic-topological invariants. We determine the first cohomology groups of flows with simply connected acting groups and those of topologically free flows having a free cycle. As an application we show that minimal extensions of such flows not only exist, but also have a rich algebraic structure.