English

On symmetric commutator subgroups, braids, links and homotopy groups

Algebraic Topology 2010-02-03 v1 Group Theory Geometric Topology

Abstract

In this paper, we investigate some applications of commutator subgroups to homotopy groups and geometric groups. In particular, we show that the intersection subgroups of some canonical subgroups in certain link groups modulo their symmetric commutator subgroups are isomorphic to the (higher) homotopy groups. This gives a connection between links and homotopy groups. Similar results hold for braid and surface groups.

Keywords

Cite

@article{arxiv.1002.0429,
  title  = {On symmetric commutator subgroups, braids, links and homotopy groups},
  author = {J. Y. Li and J. Wu},
  journal= {arXiv preprint arXiv:1002.0429},
  year   = {2010}
}

Comments

24 pages, 1 figure

R2 v1 2026-06-21T14:42:19.292Z