Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orientable 4-dimensional Poincar\'e Complexes have Reducible Spivak
  Fibrations   We show that the Spivak normal fibration of an orientable 4-dimensional
Poincar\'e complex has a vector bundle reduction.

25
The categories of this paper are: patt-sol
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The categories of this paper are: stat
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph