A new construction of lens spaces

Let Tn be the real n-torus group. We introduce a new definition of lens spaces and give some sufficient conditions for diffeomorphic classification of lens spaces. We show that any 3-dimensional lens space L(p;q) is T2-equivariantly cobordant to zero. We also give some sufficient conditions for higher dimensional lens spaces L(p;q1,…,qn) to be Tn+1-equivariantly cobordant to zero. General results in equivariant topology imply that torus equivariant complex bordism classes of lens spaces are trivial. In contrast, our proofs are constructive using toric topological arguments.