## Algebraic & Geometric Topology

### On the third homotopy group of Orr's space

#### Abstract

K Orr defined a Milnor-type invariant of links that lies in the third homotopy group of a certain space $K ω$. 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 18, Number 1 (2018), 569-582.

Dates
Revised: 2 July 2017
Accepted: 13 July 2017
First available in Project Euclid: 1 February 2018

https://projecteuclid.org/euclid.agt/1517454226

Digital Object Identifier
doi:10.2140/agt.2018.18.569

Mathematical Reviews number (MathSciNet)
MR3748253

Zentralblatt MATH identifier
1383.55010

#### Citation

Dror Farjoun, Emmanuel; Mikhailov, Roman. On the third homotopy group of Orr's space. Algebr. Geom. Topol. 18 (2018), no. 1, 569--582. doi:10.2140/agt.2018.18.569. https://projecteuclid.org/euclid.agt/1517454226

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