Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Whitehead theorem for periodic homotopy groups   We show that $v_n$-periodic homotopy groups detect homotopy equivalences
between simply-connected finite CW-complexes.

15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg