Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A short exposition of the Levine-Lidman example of spineless 4-manifolds   A 2018 paper by A. Levine and T. Lidman outlines a proof of the following
interesting result in topology of manifolds: there is a compact smooth
4-manifold $W$ with boundary such that $W$ is homotopy equivalent to $S^2$ but
there does not exist an embedding $S^2\to W$ which is a homotopy equivalence
and is simplicial for some triangulations of $W$ and of $S^2$.
  We present a shorter (and hopefully clearer) exposition. We reveal that some
parts of the proof are missing, and that some results are used in that paper
without proof or reference, or even without explicit statement.

14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
20
The categories of this paper are: acc-phys