Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On symmetric commutator subgroups, braids, links and homotopy groups   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.

35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs