Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: First cohomology of pure mapping class groups of big genus one and zero
  surfaces   We prove that the first integral cohomology of pure mapping class groups of
infinite type genus one surfaces is trivial. For genus zero surfaces we prove
that not every homomorphism to $\mathbb{Z}$ factors through a sphere with
finitely many punctures. In fact we get an uncountable family of such maps.

8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
10
The categories of this paper are: q-bio
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat