Geodesic
On intersecting subgroups of Brunnian link groups
Lei, Fengchun1 ; Wu, Jie2 ; Zhang, Yu3
1School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China
2Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
3Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China
Algebraic and Geometric Topology, Tome 16 (2016) no. 2, pp. 1043-1061
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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 ∏ σ∈Σm[[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.

DOI : 10.2140/agt.2016.16.1043
Classification : 55Q40, 57M25
Keywords: Brunnian link, homotopy colimit, link group, symmetric commutator subgroup

Lei, Fengchun  1   ; Wu, Jie  2   ; Zhang, Yu  3

1 School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China
2 Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore 119076, Singapore
3 Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China 
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Lei, Fengchun; Wu, Jie; Zhang, Yu. On intersecting subgroups of Brunnian link groups. Algebraic and Geometric Topology, Tome 16 (2016) no. 2, pp. 1043-1061. doi: 10.2140/agt.2016.16.1043

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