Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $PD_3$-complexes bound   We show that every $PD_3$-complex $P$ is the boundary of a $PD_4$-pair
$(Z,P)$. If $P$ is orientable we may assume that $\pi_1(Z)=1$. We show also
that if $P$ has a manifold 1-skeleton the it is homotopy equivalent to a closed
3-manifold.

34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph