Volume 16, issue 2 (2016)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
On intersecting subgroups of Brunnian link groups

Fengchun Lei, Jie Wu and Yu Zhang

Algebraic & Geometric Topology 16 (2016) 1043–1061
Abstract

Let G(Ln) be the link group of a Brunnian n–link Ln and Ri be the normal closure of the ith meridian in G(Ln) for 1 i n. In this article, we show that the intersecting subgroup R1 R2 Rm coincides with the iterated symmetric commutator subgroup σΣm[[Rσ(1),Rσ(2)],,Rσ(m)] for 2 m n using the techniques of homotopy theory. Moreover, we give a presentation for the intersecting subgroup R1 R2 Rn.

Keywords
Brunnian link, homotopy colimit, link group, symmetric commutator subgroup
Mathematical Subject Classification 2010
Primary: 55Q40
Secondary: 57M25
References
Publication
Received: 8 April 2015
Accepted: 27 July 2015
Published: 26 April 2016
Authors
Fengchun Lei
School of Mathematical Sciences
Dalian University of Technology
Dalian, 116024
China
Jie Wu
Department of Mathematics
National University of Singapore
10 Lower Kent Ridge Road
Singapore 119076
Singapore
Yu Zhang
Department of Mathematics
Harbin Institute of Technology
Harbin, 150001
China