Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Dehn surgeries on knots in $S^3$   We show that on a hyperbolic knot $K$ in $S^3$, the distance between any two
finite surgery slopes is at most two and consequently there are at most three
nontrivial finite surgeries. Moreover in case that $K$ admits three nontrivial
finite surgeries, $K$ must be the pretzel knot $P(-2,3,7)$. In case that $K$
admits two noncyclic finite surgeries or two finite surgeries at distance two,
the two surgery slopes must be one of ten or seventeen specific pairs
respectively. For $D$-type finite surgeries, we improve a finiteness theorem
due to Doig by giving an explicit bound on the possible resulting prism
manifolds, and also prove that $4m$ and $4m+4$ are characterizing slopes for
the torus knot $T(2m+1,2)$ for each $m\geq 1$.

31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
19
The categories of this paper are: eess
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an