Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Isotopy and equivalence of knots in 3-manifolds   We show that in a prime, closed, oriented 3-manifold M, equivalent knots are
isotopic if and only if the orientation preserving mapping class group is
trivial. In the case of irreducible, closed, oriented $3$-manifolds we show the
more general fact that every orientation preserving homeomorphism which
preserves free homotopy classes of loops is isotopic to the identity. In the
case of $S^1\times S^2$, we give infinitely many examples of knots whose
isotopy classes are changed by the Gluck twist.

19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org