  For each rational homology 3-sphere $Y$ which bounds simply connected
definite 4-manifolds of both signs, we construct an infinite family of
irreducible rational homology 3-spheres which are homology cobordant to $Y$ but
cannot bound any simply connected definite 4-manifold. As a corollary, for any
coprime integers $p,q$, we obtain an infinite family of irreducible rational
homology 3-spheres which are homology cobordant to the lens space $L(p,q)$ but
cannot obtained by a knot surgery.
