Original sentence: Assume all manifolds are smooth and oriented.is possible to choose RP
Edited sentence: -dimensional real projective space.Assume all manifolds are oriented.For example, for any.The low-dimensional unoriented cobordism groups are.The mod2 Euler characteristic.The mod2 Euler characteristic map  is onto for all , and an isomorphism for.The theory was originally developed for smooth (i.differentiable) manifolds, but there are now also versions for piecewise-linear and topological manifolds.is possible to choose , the cobordism class of the.of an unoriented -dimensional manifold  is an unoriented cobordism invariant