Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The classifying space of the 1+1 dimensional $G$-cobordism category   For a finite group $G$, we define the $G$-cobordism category in dimension
two. We show there is a one-to-one correspondence between the connected
components of its classifying space and the abelianization of $G$. Also, we
find an isomorphism of its fundamental group onto the direct sum
$\mathbb{Z}\oplus \Omega_2^{SO}(BG)$, where $\Omega_2^{SO}(BG)$ is the free
oriented $G$-bordism group in dimension two, and we study the classifying space
of some important subcategories. We obtain the classifying space has the
homotopy type of the product $G/[G,G]\times S^1\times X^G$, where
$\pi_1(X^G)=\Omega_2^{SO}(BG)$. Finally, we present some results about the
classification of $G$-topological quantum field theories in dimension two.

21
The categories of this paper are: adap-org
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th