  Let $T^n$ be the real $n$-torus group. We give a new definition of lens
spaces and study the diffeomorphic classification of lens spaces. We show that
any $3$-dimensional lens space $L(p; q)$ is $T^2$-equivariantly cobordant to
zero. We also give some sufficient conditions for higher dimensional lens
spaces $L(p; q_1, \ldots, q_n)$ to be $T^{n+1}$-equivariantly cobordant to
zero. In 2005, B. Hanke showed that complex equivariant cobordism class of a
lens space is trivial. Nevertheless, our proofs are constructive using toric
topological arguments.
