Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On rack colorings for surface-knot diagrams without branch points   Racks do not give us invariants of surface-knots in general. For example, if
a surface-knot diagram has branch points (and a rack which we use satisfies
some mild condition), then it admits no rack colorings. In this paper, we
investigate rack colorings for surface-knot diagrams without branch points and
prove that rack colorings are invariants of $S^2$-knots. We also prove that
rack colorings for $S^2$-knots can be interpreted in terms of quandles, and
discuss a relationship with regular-equivalences of surface-knot diagrams.

22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex