On symmetric commutator subgroups, braids, links and homotopy groups

Details On symmetric commutator subgroups, braids, links and homotopy groups On symmetric commutator subgroups, braids, links and homotopy groups

2010-02-02

arxiv.org/abs/1002.0429v1

Mathematics

Algebraic Topology

24 pages, 1 figure

Scientific paper

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.

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