Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinitely many knots admitting the same integer surgery and a
  4-dimensional extension   We prove that for any integer $n$ there exist infinitely many different knots
in $S^3$ such that $n$-surgery on those knots yields the same 3-manifold. In
particular, when $|n|=1$ homology spheres arise from these surgeries. This
answers Problem 3.6(D) on the Kirby problem list. We construct two families of
examples, the first by a method of twisting along an annulus and the second by
a generalization of this procedure. The latter family also solves a stronger
version of Problem 3.6(D), that for any integer $n$, there exist infinitely
many mutually distinct knots such that 2-handle addition along each with
framing $n$ yields the same 4-manifold.

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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
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The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
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The categories of this paper are: chao-dyn