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