Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Cusp equivalence between smooth embeddings of the 2-sphere in 4-space   If the fundamental group of the complement of a smooth embedding f: S^2
\subset R^4 is a cyclic group, the map can be deformed to the standard
embedding by a generic one-parameter family with at most cusp singularities. If
two smooth embeddings are connected by such a deformation, they will be called
cusp equivalent. We will discuss the relation of three equivalences of smooth
2-knots S^2 \subset R^4; cusp equivalence, stable equivalence and weakly stable
equivalence.

9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc