Abstract
Let
M
n
be the set of equivariant unoriented cobordism classes of all
n
-dimensional 2-torus manifolds, where an
n
-dimensional 2-torus manifold
M
is a smooth closed manifold of dimension
n
with effective smooth action of a rank
n
2-torus group
(
Z
2
)
n
. Then
M
n
forms an abelian group with respect to disjoint union. This paper determines the group structure of
M
n
and shows that each class of
M
n
contains a small cover as its representative in the case
n=3
.