Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Spectra of Volume and Determinant Densities of Links   The $\textit{volume density}$ of a hyperbolic link $K$ is defined to be the
ratio of the hyperbolic volume of $K$ to the crossing number of $K$. We show
that there are sequences of non-alternating links with volume density
approaching $v_8$, where $v_8$ is the volume of the ideal hyperbolic
octahedron. We show that the set of volume densities is dense in $[0,v_8]$. The
$\textit{determinant density}$ of a link $K$ is $[2 \pi \log \det(K)]/c(K)$. We
prove that the closure of the set of determinant densities contains the set
$[0, v_8]$.

9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an