Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 3-manifolds and 4-dimensional surgery   Let $X$ be a connected compact 3-manifold with non-empty boundary. Consider
the boundary $M$ of $X\times D^2$. $M$ is a 4-dimensional closed manifold and
has the same fundamental group as $X$. Various examples of $X$ are known for
which a certain assembly map $A:H_4(X;L)\to L_4(\pi_1(X))$ is injective. For
such an $X$ and any CW-spine $B$ of $X$, there is a $UV^1$-map $p:M\to B$. For
any $\epsilon>0$, if the surgery obstruction for a TOP normal map $(f,b):N\to
M$ vanishes, we can perform surgery on $f$ to change it into a
$p^{-1}(\epsilon)$-controlled homotopy equivalence.

24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat