Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: 3-manifolds lying in trisected 4-manifolds   The spine of a trisected 4-manifold is a singular 3-dimensional set from
which the trisection itself can be reconstructed. 3-manifolds embedded in the
trisected 4--manifold can often be isotoped to lie almost or entirely in the
spine of the trisection. We define this notion and show that in fact every
3-manifold can be embedded to lie almost in the spine of a minimal genus
trisection of some connect sum of $S^2 \tilde \times S^2$s. This mirrors the
known fact that every 3-manifold can be smoothly embedded in a connect sum of
$S^2 \times S^2$s. Our methods additionally give an upper bound for how many
copies of $S^2 \tilde \times S^2$ based on a distance calculated in an
appropriately defined graph. For the special case of lens spaces we analyze
more closely and obtain more explicit bounds.

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The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
1
The categories of this paper are: cs
22
The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
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The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int