On the third homotopy group of Orr's space
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grouphomotopythirdlinksopenspacebeencertain
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K. Orr defined a Milnor-type invariant of links that lies in the third homotopy group of a certain space $K_\omega.$ The problem of non-triviality of this third homotopy group has been open. We show that it is an infinitely generated group. The question of realization of its elements as links remains open.
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