Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nullification of knots and links   In this paper, we study a geometric/topological measure of knots and links
called the nullification number. The nullification of knots/links is believed
to be biologically relevant. For example, in DNA topology, one can intuitively
regard it as a way to measure how easily a knotted circular DNA can unknot
itself through recombination of its DNA strands. It turns out that there are
several different ways to define such a number. These definitions lead to
nullification numbers that are related, but different. Our aim is to explore
the mathematical properties of these nullification numbers. First, we give
specific examples to show that the nullification numbers we defined are
different. We provide detailed analysis of the nullification numbers for the
well known 2-bridge knots and links. We also explore the relationships among
the three nullification numbers, as well as their relationships with other knot
invariants. Finally, we study a special class of links, namely those links
whose general nullification number equals one. We show that such links exist in
abundance. In fact, the number of such links with crossing number less than or
equal to n grows exponentially with respect to n.

30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
23
The categories of this paper are: solv-int
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics