In this talk, we discuss whether a conformal class on the boundary M of a given compact manifold X can be the conformal infinity of a Poincaré-Einstein metric in X. We construct an invariant of conformal classes on the boundary M of a compact spin manifold X of dimension 4k with the help of the Dirac operator. We prove that a conformal class cannot be the conformal infinity of a Poincaré-Einstein metric if this invariant is not zero. Furthermore, we will prove this invariant can attain values of infinitely many integers if one invariant is not zero on the above given spin manifold. This talk is based on a joint work with Gursky and Stolz.