Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Observed periodicity related to the four-strand Burau representation   A long-standing open problem is to determine for which values of n the Burau
representation Psi_n of the braid group B_n is faithful. Following work of
Moody, Long-Paton, and Bigelow, the remaining open case is n = 4. One criterion
states that Psi_n is unfaithful if and only if there exists a pair of arcs in
the n-punctured disk D_n such that a certain associated polynomial is zero. In
this paper, we use a computer search to show that there is no such arc-pair in
D_4 with 2000 or fewer intersections, thus certifying the faithfulness of Psi_4
up to this point. We also investigate the structure of the set of arc-pair
polynomials, observing a striking periodicity that holds between those that
are, in some sense, 'closest' to zero. This is the first instance known to the
authors of a deeper analysis of this polynomial set.

1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
17
The categories of this paper are: q-fin
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys