On intersecting subgroups of Brunnian link groups

Lei, Fengchun; Wu, Jie; Zhang, Yu

doi:10.2140/agt.2016.16.1043

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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

DOI: 10.2140/agt.2016.16.1043

Abstract

Let $G (L_{n})$ be the link group of a Brunnian $n$ –link $L_{n}$ and $R_{i}$ be the normal closure of the $i^{t h}$ meridian in $G (L_{n})$ for $1 \leq i \leq n$ . In this article, we show that the intersecting subgroup $R_{1} \cap R_{2} \cap \dots \cap R_{m}$ coincides with the iterated symmetric commutator subgroup $\prod_{σ \in Σ_{m}} [[R_{σ (1)}, R_{σ (2)}], \dots, R_{σ (m)}]$ for $2 \leq m \leq n$ using the techniques of homotopy theory. Moreover, we give a presentation for the intersecting subgroup $R_{1} \cap R_{2} \cap \dots \cap R_{n}$ .

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

Volume 16, issue 2 (2016)