Algebraic & Geometric Topology

On intersecting subgroups of Brunnian link groups

Fengchun Lei, Jie Wu, and Yu Zhang

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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.

Article information

Source
Algebr. Geom. Topol., Volume 16, Number 2 (2016), 1043-1061.

Dates
Received: 8 April 2015
Accepted: 27 July 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841160

Digital Object Identifier
doi:10.2140/agt.2016.16.1043

Mathematical Reviews number (MathSciNet)
MR3493415

Zentralblatt MATH identifier
1337.55013

Subjects
Primary: 55Q40: Homotopy groups of spheres
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
Brunnian link homotopy colimit link group symmetric commutator subgroup

Citation

Lei, Fengchun; Wu, Jie; Zhang, Yu. On intersecting subgroups of Brunnian link groups. Algebr. Geom. Topol. 16 (2016), no. 2, 1043--1061. doi:10.2140/agt.2016.16.1043. https://projecteuclid.org/euclid.agt/1510841160


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