Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Diagram uniqueness for highly twisted knots   Frequently, knots are enumerated by their crossing number. However, the
number of knots with crossing number $c$ grows exponentially with $c$, and to
date computer-assisted proofs can only classify diagrams up to around twenty
crossings. Instead, we consider diagrams enumerated by bridge number, following
the lead of Schubert who classified 2-bridge knots in the 1950s. We prove a
uniqueness result for this enumeration. Using recent developments in geometric
topology, including distances in the curve complex and techniques with
incompressible surfaces, we show that infinitely many knot and link diagrams
have a unique simple $m$-bridge diagram. Precisely, if $m$ is at least three,
if each twist region of the diagram has at least three crossings, and if the
length $n$ of the diagram is sufficiently long, i.e., $n>4m(m-2)$, then such a
diagram is unique up to obvious rotations. This projection gives a canonical
form for such knots and links, and thus provides a classification of these
knots or links.

17
The categories of this paper are: q-fin
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat