Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Applications of controlled surgery in dimension 4: Examples   The validity of Freedman's disk theorem is known to depend only on the
fundamental group. It was conjectured that it fails for nonabelian free
fundamental groups. If this were true then surgery theory would work in
dimension four. Recently, Krushkal and Lee proved a surprising result that
surgery theory works for a large special class of 4-manifolds with free
nonabelian fundamental groups. The goal of this paper is to show that this also
holds for other fundamental groups which are not known to be good, and that it
is best understood using controlled surgery theory of Pedersen--Quinn--Ranicki.
We consider some examples of 4-manifolds which have the fundamental group
either of a closed aspherical surface or of a 3-dimensional knot space. A more
general theorem is stated in the appendix.

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The categories of this paper are: adap-org
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: solv-int