Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Equivariant Bordism of 2-Torus Manifolds and Unitary Toric Manifolds   The equivariant bordism classification of manifolds with group actions is an
essential subject in the study of transformation groups. We are interesting in
the action of 2-torus group $\mathbb{Z}_2^n$ and torus group $T^n$, and study
the equivariant bordism of 2-torus manifolds and unitary toric manifolds. In
this paper, we give a new description of the group
$\mathcal{Z}_n(\mathbb{Z}_2^n)$ of 2-torus manifolds, and determine the
dimention of $\mathcal{Z}_n(\mathbb{Z}_2^n)$ as a $\mathbb{Z}_2$-vector space.
With the help of toric topology, L\"u and Tan proved that the bordism groups
$\mathcal{Z}_n(\mathbb{Z}_2^n)$ are generated by small covers. We will give a
new proof to this result. These results can be generalized to the equivariant
bordism of unitary toric manifolds, that is, we will give a new description of
the group $\mathcal{Z}_n^U(T^n)$ of unitary torus manifolds, and prove that
$\mathcal{Z}_n^U(T^n)$ can be generated by quasitoric manifolds with
omniorientations.

0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
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
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat