Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $PD_3$-pairs with compressible boundary   We extend work of Turaev and Bleile to relax the $\pi_1$-injectivity
hypothesis in the characterization of the fundamental triples of $PD_3$-pairs
with aspherical boundary components. This is further extended to pairs
$(P,\partial{P})$ which also have spherical boundary components and with
$c.d.\pi_1(P)\leq2$.

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The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol