Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Critical Heegaard surfaces obtained by self-amalgamation   Critical surfaces can be regarded as topological index 2 minimal surfaces
which was introduced by David Bachman. In this paper we give a sufficient
condition and a necessary condition for self-amalgamated Heegaard surfaces to
be critical.

34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org