Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite Type Invariants of w-Knotted Objects I: w-Knots and the Alexander
  Polynomial   This is the first in a series of papers studying w-knotted objects (w-knots,
w-braids, w-tangles, etc.), which make a class of knotted objects which is
{w}ider but {w}eaker than their usual counterparts.
  The group of w-braids was studied (as "{w}elded braids") by
Fenn-Rimanyi-Rourke and was shown to be isomorphic to the McCool group of
"basis-conjugating" automorphisms of a free group Fn. Brendle-Hatcher, tracing
back to Goldsmith, have shown this group to be a group of movies of flying
rings in R3. Satoh studied several classes of w-knotted objects (as
"{w}eakly-virtual") and has shown them to be closely related to certain classes
of knotted surfaces in R4. So w-knotted objects are algebraically and
topologically interesting.
  Here we study finite type invariants of w-knotted objects. Following
Berceanu-Papadima, we construct homomorphic universal finite type invariants
("expansions") of w-braids and of w-tangles. We find that the universal finite
type invariant of w-knots is essentially the Alexander polynomial.
  We find that the spaces Aw of "arrow diagrams" for w-knotted objects are
related to not-necessarily-metrized Lie algebras. Many questions concerning
w-knotted objects turn out to be equivalent to questions about Lie algebras.
Most notably we find that a homomorphic expansion of w-knotted foams is
essentially the same as a solution of the Kashiwara-Vergne conjecture (KV),
thus giving a topological explanation to the work of Alekseev-Torossian work on
KV and Drinfel'd associators.
  The true value of w-knots, though, is likely to emerge later, for we expect
them to serve as a {w}armup example for the study of virtual knots. We expect
v-knotted objects to provide the global context whose associated graded
structure will be the Etingof-Kazhdan theory of quantization of Lie bialgebras.

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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-th
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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: stat
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci