Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Seifert Klein bottles for knots with common boundary slopes   We consider the question of how many essential Seifert Klein bottles with
common boundary slope a knot in S^3 can bound, up to ambient isotopy. We prove
that any hyperbolic knot in S^3 bounds at most six Seifert Klein bottles with a
given boundary slope. The Seifert Klein bottles in a minimal projection of
hyperbolic pretzel knots of length 3 are shown to be unique and pi_1-injective,
with surgery along their boundary slope producing irreducible toroidal
manifolds. The cable knots which bound essential Seifert Klein bottles are
classified; their Seifert Klein bottles are shown to be non-pi_1-injective, and
unique in the case of torus knots. For satellite knots we show that, in
general, there is no upper bound for the number of distinct Seifert Klein
bottles a knot can bound.

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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: math-ph