Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bridge distance and plat projections   We calculate the bridge distance for $m$-bridge knots/links in the $3$-sphere
with sufficiently complicated $2m$-plat projections. In particular we show that
if the underlying braid of the plat has $n - 1$ rows of twists and all its
exponents have absolute value greater than or equal to three then the distance
of the bridge sphere is exactly $\lceil n/(2(m - 2)) \rceil$, where $\lceil x
\rceil$ is the smallest integer greater than or equal to $x$. As a corollary,
we conclude that if such a diagram has more than $4m(m-2)$ rows then the bridge
sphere defining the plat projection is the unique minimal bridge sphere for the
knot.

29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
3
The categories of this paper are: physics