Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Clustering of critical points in Lefschetz fibrations and the symplectic
  Szpiro inequality   We prove upper bounds for the number of critical points in semistable
symplectic Lefschetz fibrations. We also obtain a new lower bound for the
number of nonseparting vanishing cycles in Lefschetz pencils, and reprove the
known lower bounds for the commutator lengths of Dehn twists.

23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc