Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: P versus NP and geometry   I describe three geometric approaches to resolving variants of P v. NP,
present several results that illustrate the role of group actions in complexity
theory, and make a first step towards completely geometric definitions of
complexity classes.

33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph