Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the union stabilization of two Heegaard splittings   Let two Heegaard splittings $V_1 \cup W_1$ and $V_2 \cup W_2$ of a 3-manifold
$M$ be given. We consider the union stabilization $M=V \cup W$ which is a
common stabilization of $V_1 \cup W_1$ and $V_2 \cup W_2$ having the property
that $V=V_1 \cup V_2$. We show that any two Heegaard splittings of a 3-manifold
have a union stabilization. We also give some examples with numerical bounds on
the minimal genus of union stabilization. On the other hand, we give an example
of a candidate for which the minimal genus of union stabilization is strictly
larger than the usual stable genus -- the minimal genus of common
stabilization.

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The categories of this paper are: q-alg
14
The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: alg-geom