Volume 16, issue 2 (2016)

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On intersecting subgroups of Brunnian link groups

Fengchun Lei, Jie Wu and Yu Zhang

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

Let $G\left({L}_{n}\right)$ be the link group of a Brunnian $n$–link ${L}_{n}$ and ${R}_{i}$ be the normal closure of the ${i}^{th}$ meridian in $G\left({L}_{n}\right)$ for $1\le i\le n$. In this article, we show that the intersecting subgroup ${R}_{1}\cap {R}_{2}\cap \cdots \cap {R}_{m}$ coincides with the iterated symmetric commutator subgroup ${\prod }_{\sigma \in {\Sigma }_{m}}\left[\left[{R}_{\sigma \left(1\right)},{R}_{\sigma \left(2\right)}\right],\dots ,{R}_{\sigma \left(m\right)}\right]$ for $2\le m\le n$ using the techniques of homotopy theory. Moreover, we give a presentation for the intersecting subgroup ${R}_{1}\cap {R}_{2}\cap \cdots \cap {R}_{n}$.