Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stabilizing Heegaard splittings of toroidal 3-manifolds   Let $T$ be a separating incompressible torus in a 3-manifold $M$. Assuming
that a genus $g$ Heegaard splitting $V \cup_S W$ can be positioned nicely with
respect to $T$ (e.g. $V \cup_S W$ is strongly irreducible), we obtain an upper
bound on the number of stabilizations required for $V \cup_S W$ to become
isotopic to a Heegaard splitting which is an amalgamation along $T$. In
particular, if $T$ is a canonical torus in the JSJ decomposition of $M$, then
the number of necessary stabilizations is at most $4g-4$. As a corollary, this
establishes an upper bound on the number of stabilizations required for $V
\cup_S W$ and any Heegaard splitting obtained by a Dehn twist of $V \cup_S W$
along $T$ to become isotopic.

15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con