Algebraic & Geometric Topology

On the third homotopy group of Orr's space

Emmanuel Dror Farjoun and Roman Mikhailov

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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
Received: 30 March 2017
Revised: 2 July 2017
Accepted: 13 July 2017
First available in Project Euclid: 1 February 2018

Permanent link to this document
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

Subjects
Primary: 55Q52: Homotopy groups of special spaces 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
link invariants homotopy groups Orr invariant

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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