Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Distance one surgeries on the lens space $L(n,1)$   In this paper, we show that the lens space $L(s,1)$ for $s \neq 0 $ is
obtained by a distance one surgery along a knot in the lens space $L(n,1)$ with
$n \geq 5$ odd only if $n$ and $s$ satisfy one of the following cases: (1) $n
\geq 5$ is any odd integer and $s=\pm 1, n, n \pm 1$ or $n \pm 4$; (2) $n=5$
and $s=-5$; (3) $n=5$ and $s=-9$; (4) $n=9$ and $s=-5$. As a corollary, we
prove that the torus link $T(2,s)$ for $s \neq 0 $ is obtained by a band
surgery from $T(2,n)$ with $n \geq 5$ odd only if $n$ and $s$ are as listed
above. Combined with the result of Lidman, Moore and Vazquez, it immediately
follows that the only nontrivial torus knot $T(2,n)$ admitting chirally
cosmetic banding is $T(2,5)$. The key ingredient of our proof is the Heegaard
Floer mapping cone formula.

24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin