Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The lens space realization problem   We determine the lens spaces that arise by integer Dehn surgery along a knot
in the three-sphere. Specifically, if surgery along a knot produces a lens
space, then there exists an equivalent surgery along a Berge knot with the same
knot Floer homology groups. This leads to sharp information about the genus of
such a knot. The arguments rely on tools from Floer homology and lattice
theory, and are primarily combinatorial in nature.

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
9
The categories of this paper are: nlin
3
The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: econ
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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: acc-phys
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga