Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The (n)-solvable filtration of the link concordance group and Milnor's
  invariants   We establish several new results about both the (n)-solvable filtration,
F_n^m, of the set of link concordance classes and the (n)-solvable filtration
of the string link concordance group. We first establish a relationship between
Milnor's invariants and links, L, with certain restrictions on the 4-manifold
bounded by M_L. Using this relationship, we can relate (n)-solvability of a
link (or string link) with its Milnor's invariants. Specifically, we show that
if a link is (n)-solvable, then its Milnor's invariants vanish for lengths up
to 2^{n+2}-1. Previously, there were no known results about the "other half" of
the filtration, namely F_{n.5}^m/F_{n+1}^m. We establish the effect of the Bing
doubling operator on (n)-solvability and using this, we show that
F_{n.5}^m/F_{n+1}^m is nontrivial for links (and string links) with
sufficiently many components. Moreover, we show that these quotients contain an
infinite cyclic subgroup. We also show that links and string links modulo
(1)-solvability is a nonabelian group. We show that we can relate other
filtrations with Milnor's invariants. We show that if a link is n-positive,
then its Milnor's invariants will also vanish for lengths up to 2^{n+2}-1.
Lastly, we prove that the Grope filtration, G_n^m, of the set of link
concordance classes is not the same as the (n)-solvable filtration.

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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ph