Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Surface Homeomorphisms That Do Not Extend to Any Handlebody and the
  Johnson Filtration   We prove the existence of homeomorphisms of a closed, orientable surface of
genus 3 or greater that do not extend to any handlebody bounded by the surface.
We show that such homeomorphisms exist arbitrarily deep in the Johnson
filtration of the mapping class group. The second and third terms of the
Johnson filtration are the well-known Torelli group and Johnson subgroup,
respectively. Richard Hain has obtained very similar results by different
methods.

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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: atom-ph