Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effect of a crossing change on crossing number   The purpose of this article is to give a preliminary clarification on the
relation between crossing number and crossing change. With a main focus on the
span of X polynomial, we prove that, as our theorem claims, the crossing number
of the link after crossing change can be estimated when certain conditions are
met. At the end of the article, we give an example to demonstrate a special
case for the theorem and a counterexample to explain that the theorem cannot be
applied if the obtained link is not alternating.

31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs