#### Volume 18, issue 1 (2018)

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On the third homotopy group of Orr's space

### Emmanuel Dror Farjoun and Roman Mikhailov

Algebraic & Geometric Topology 18 (2018) 569–582
##### Abstract

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 nontriviality 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.

##### Keywords
link invariants, homotopy groups, Orr invariant
##### Mathematical Subject Classification 2010
Primary: 55Q52, 57M25