Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-integer characterizing slopes for torus knots   A slope $p/q$ is a characterizing slope for a knot $K$ in $S^3$ if the
oriented homeomorphism type of $p/q$-surgery on $K$ determines $K$ uniquely. We
show that for each torus knot its set of characterizing slopes contains all but
finitely many non-integer slopes. This generalizes work of Ni and Zhang who
established such a result for $T_{5,2}$. Along the way we show that if two
knots $K$ and $K'$ in $S^3$ have homeomorphic $p/q$-surgeries, then for $q\geq
3$ and $p$ sufficiently large we can conclude that $K$ and $K'$ have the same
genera and Alexander polynomials. This is achieved by consideration of the
absolute grading on Heegaard Floer homology.

24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph