Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degree one cohomology with twisted coefficients of the mapping class
  group   Let $\Gamma$ be the mapping class group of an oriented surface $\Sigma$ of
genus g with r boundary components. We prove that the first cohomology group
$H^1(\Gamma, O(M_{SL(2, C)})^*)$ is non-trivial, where the coefficient module
is the dual of the space of algebraic functions on the $SL(2, C)$ moduli space
over $\Sigma$.

13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys