Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extending homeomorphisms from 2-punctured surfaces to handlebodies   Let F a closed connected orientable surface bounding a genus g handlebody H.
In this paper we find a finite set of generators for the subgroup E(2,g) of the
pure mapping class group of the twice punctured torus PMCG(2,g), consisting of
the isotopy classes of homeomorphisms of F which admit an extension to H
keeping a properly embedded trivial arc fixed. This subgroup turns out to be
important for the study of knots in closed 3-manifolds via (g,1)-decomposition.
In fact, the knots represented by the isotopy classes belonging to the same
left cosets of E(2,g) in PMCG(2,g) are equivalent.

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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con