Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some notes on the inverse problem for braids   The Kontsevich integral $Z$ associates to each braid $b$ (or more generally
knot $k$) invariants $Z_i(b)$ lying in finite dimensional vector spaces, for $i
= 0, 1, 2, ...$. These values are not yet known, except in special cases. The
inverse problem is that of determining $b$ from its invariants $Z_i(b)$.
  In this paper we study the case of braids on two strands, which is already
sufficient to produce interesting and unexpected mathematics. In particular, we
find connections with number theory, numerical analysis and field theory in
physics. However, we will carry this study out with an eye to the more general
case of braids on $n$ strands. We expect that solving the inverse problem even
for $n=3$ will present real difficulties. Most of the concepts in this paper
also apply to knots, but to simplify the exposition we will rarely mention
this.
  The organisation and bulk of the writing of this paper predates its most
significant results. We hope later to present better and develop further these
results.

0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas