Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homotopy invariants of Gauss phrases   Equivalence relations can be defined on Gauss phrases using combinatorial
moves. In this paper we consider two closely related equivalence relations on
Gauss phrases, homotopy and open homotopy. In particular, in each case, we
define a new invariant and determine the values that it can attain.

30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas