Volume 18, issue 1 (2018)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 Kω . 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
References
Publication
Received: 30 March 2017
Revised: 2 July 2017
Accepted: 13 July 2017
Published: 10 January 2018
Authors
Emmanuel Dror Farjoun
Department of Mathematics
Hebrew University of Jerusalem
Jerusalem, Israel
Roman Mikhailov
Chebyshev Laboratory
Saint Petersburg State University
Saint Petersburg, Russia
Saint Petersburg Department of Steklov Mathematical Institute
Saint Petersburg, Russia
School of Mathematics
Tata Institute of Fundamental Research
Mumbai, India